It is great to hear from an innovator! I feel I've been in your shoes and hence can answer your questions. Each of your bullet points has a heading here:
EU / worldwide patents
No, you cannot file a worldwide patent in your country. The general idea is that every country has its own patent system, and you need to file in every country where you do want patent protection. This may not make much practical difference for you, as naturally you can file in every nation you want without ever leaving your country. But it does mean that each application is separate and incurs separate fees.
The EU is, as so often, a special case in that it is indeed possible to apply for EU-wide patent protection in just a single EU country, and this is not significantly more expensive than filing for patent protection only for your own country.
Worldwide patent protection is often, despite what you may think, not required. The patent protects against using something. That usually includes commercial use. So even if some rogue state hosts a business refusing to honor your foreign patent, they will typically only be legally allowed to do so in their own little country. As soon as they sell their service or products to the US or the EU, you can sue them (or their importer or reseller) there, even if you only have patent protection in the US or only in the EU. In fact, "selling" is not even necessary, but then you may have to find a way to put a price tag on the damages done that convinces a court.
Technically, you do not need a patent attorney to file a patent; all this person would do is, essentially, to avoid beginner's mistakes. He will have more experience in doing all the things you should do anyways, and probably already have. In particular, I'm thinking about patent research (has the idea or aspects of it already been patented or published?) and formulating your claims. The details here determine just what is protected, how defensible the patent is in court, and what chances you have to salvage some claims if others are found invalid or you choose not to defend them in court. I suppose there is a chance that a patent attorney might also be able to help, at least with contacts, towards monetizing your patent (assuming you are willing to consider giving licenses).
Sorry, I don't know. It happens; historically, patents for perpetuum mobiles have been consistently denied. In recent decades, however, you'll easily find people expressing concern that many patents have been granted for ideas that clearly cannot work.
In my experience, policies can be surprisingly well predicted by simply considering the incentives. Both the EU and the US have moved to financially incentivise their patent offices for granting patents, but not, as far as I know, for rejecting them or analyzing how granted patents stand up in court (which for valuable patents is usually the real test). Go figure.
My best guess is that save for obvious defects, such as a similar idea already being known or your application not conforming to some formal requirements or failing to address what is novel and useful about your idea, your chances of rejection are remote. You may take additional comfort in knowing that you would be the source of this financial incentive to grant patents: If you chose not to hire a patent attorney, your expenses will be lower for a rejected patent application than for a successful one.
I don't know if a bank in the EU would be willing to finance your patent. There's only one way to find out: Inquire!
I suspect banks would want the following:
1. A business plan detailing how and when you expect to recoup your expenses plus a profit. This could be from using your patent (but then the credit will presumably be for the business as a whole), or from a plan to sell or license use of your invention (which, again, could be seen as a business where the actual patent is merely an important part of a bigger operation).
2. Collateral. Banks, despite often curious about your intentions, are so risk adverse, they may well decide not to take a risk regarding the success of your patent venture. So they'll ask you what property or other assets (parents' ?) you're willing to (partially) bet on your success.
You may be better off getting funded by an investor. If you figure out how to attract one, let me know for my own ideas!
If you do not hire a patent attorney and do not pay yourself for your time and effort, expect to incur fees around 1 kUSD for each of the EU and the US per granted patent, not counting increasing costs for keeping the patent after five years or so. If you hire an attorney, I suppose it really depends on the actual workload your application requires. Ask! I think the figure you mentioned may well be sufficient for both a EU and a US patent application using a patent attorney.
Please appreciate that a patent is essentially a title. Depending on your intentions and other market participants, there is a certain danger that using it involves disputes, which can mean costly lawsuits, either to bring competitors to respect your patent and licensing terms, or to prevent someone else from having your patent declared invalid by court.
Time to get a patent granted
It generally takes too long. It is rather frequent for a patent to not be granted within the first 12 months of the application. Sometimes applicants seem to want to drag out the process themselves, though. Under certain conditions, you can retroactively change details of your application without changing the formal initial application dare used to decide priority. If an applicant cares more about how long to extend the patent protection in the end rather than what date the patent is formally granted, this can be advantageous. It also may allow clever legal departments to have their company file a patent before they have completely worked out all relevant aspects of what they have invented---ask your patent lawyer if ever you want to optimize to this point yourself. This is an area where knowing how to write patent claims widely to the point of being almost unacceptably broad comes in.
It would be great to get patents granted in under a year, because I believe there is a one-year grace period for you to decide in what other countries to seek patent protection besides the one where you initially applied. But please seek another source for this (patent attorney?) because I am unsure about the details; maybe this deadline only starts ticking when the patent is granted, not when you initially file for it.
Idea theft by corporations
The likelihood of your idea being stolen depends on many things. Only if you can be seen as successful or solve a problem plaguing others, there is a chance they will even want to. And only if they can easily replicate your invention can they copy it rather than be inventive themselves. So depending on whether your invention is some magic under the hood or something self-evident, and if its effect is something the big players even care to notice, the answer can range all the way from no chance at all to very likely indeed.
Despite whatever worries you may have in this regard, and despite not knowing any details of your invention, let me try to encourage you to take a much broader view. If you can come up with one great invention, you will be very useful and valuable in lots of areas. If your idea is great enough to be stolen, and not stolen by just anyone but by the big players, this could be your greatest personal breakthrough ever, towards getting future ideas funded or landing a great job. Not necessarily with a company that prefers stealing your idea rather than asking you to consult and license them in this regard, but certainly elsewhere.
I know that it probably would not seem like an adequate compensation for what must feel like the prospect of being cheated out of something that should be yours. Yet sadly, despite your expectations being the very justification for our patent laws, the reality of it just doesn't necessarily conform to the spirit of the law or one's likely views as an innovator. Being right isn't always sufficient to get the entire cake, so unless you have the legal and financial muscle to fight a corporation, you may have to settle for sharing, negotiating, or otherwise living with it.