When filing a patent, the goal of the Independent Claim(s) is to define the invention as broadly as possible. Your goal is to obtain Freedom to Operate, with enough "white space" around your Preferred Embodiment that competitors cannot change minor details to avoid licensing your patent.
Dependent claims provide paths to multiple embodiments of your invention, and also provide a means to establish Prior Art for others in the field seeking similar patents. For instance, you can anticipate some refinements or other uses that solve a related problem that a competitor might implement to work around your independent claim.
The claims in a patent application are a starting point for negotiation with the patent office on novelty and non-obviousness. Through a series of Office Actions, the Inventor (you) and the Patent Office (e.g., USPTO) negotiate to (optimally) the broadest possible coverage on the independent claims. Often, when an independent claim is too broad, clauses from dependent claims are moved into the independent claim to narrow its scope.
That said, you can have a patent with a single independent claim and no other claims. I know I've encountered one that granted, but it would be difficult to find it at the moment. A patent defined in this way might be so narrowly defined that another inventor might easily make several modifications and thus obtain Freedom to Operate in your space.
There are patents granted out there with over 400 claims. I'm uncertain what the maximum is, but if you exceed 10 or so on a PCT application, you will end up paying extra, and that cost adds up.
If you have multiple independent claims (as is common with software patents, which have similar independent claims that cover the method, the system and the hardware implementation), this may multiply the number of dependent claims as well. If your independent claims are too dissimilar to each other, or a single dependent claim adds too much novelty (e.g., a combination of 3 or more non-obvious clauses), and you are filing for an international patent, you may be required by the Examiner to file multiple applications, which will double your cost and add to the difficulty of prosecuting the patent.
In your application, you should write as many claims as you think you need to get the amount of "white space" you need to protect your invention from competition. You will probably lose a few through Office Actions. For instance, you might file 40 claims but only 10 are granted.
Yes, your claims can be rejected if they match the claims in a patent or application that has an earlier Priority Date. As a matter of fact, any material at all in any publicly accessible documents that describe the invention you are claiming can be used to reject your claims. This is why your independent claims are the most important to get right.
This brings up another important point. If your patent is ever challenged, a case might be made that additional Prior Art exists for one or more of your claims, or that some of your claims are considered "obvious". This may result in one or more of your dependent claims becoming invalid and unenforceable. Therefore, claiming multiple embodiments is a way to defend against challenges.
Typically, whole claims are used to prosecute infringement (e.g., any independent claim or a dependent claim plus all of its dependencies). However, there are a few cases out there where parts of claims were used to judge infringement. It can get complicated, which is why you should seek broad coverage.
To address your first example of the independent claim with the dependent claim, you need to answer the following questions:
- Is the independent claim novel? "Awesome equipment" may even already exist, but you may claim a novel use of it to solve a different problem (if there is no Prior Art).
- Is the independent claim non-obvious (to someone "skilled in the art")?
- Is the independent claim too abstract?
There are a lot of other possible reasons for rejection, but those are the main ones. Typically, a test for novelty is something with no Prior Art, or a combination of three or more known things arranged in a new, non-obvious way to solve a problem.
As for your second question,
For the dependent claim(s):
- Does the dependent claim achieve any technical effect? (e.g., does using a fork actually add functionality?) If not, your dependent claim may be rejected.
Now, for the second example, where the two claims are merged:
If someone else were to claim "an awesome equipment to detect X using spoon?", the same test for novelty applies. If you or someone else covered such a case anywhere in the patent application, then Prior Art exists. Is it obvious to modify your equipment using a spoon?
However, don't confuse patenting with Freedom to Operate. If your claims are not broad enough to cover the "using spoon" clause, then someone else may not be able to patent it, but they may still have Freedom to Operate.
That's about the best I can do with such an abstract hypothetical set of claims, but I hope its instructive. This is really the reason that patent lawyers exist, to assist with claim construction and help you to get the coverage you need without too many expensive Office Actions. The tests for novelty and non-obviousness are changing year-to-year (and new tests such as abstractness are added), and the patent attorneys are the ones you can rely to stay up to date on those rules.
Also, I think a great way to learn more is to read through the claims of existing patents in your space (grants, not applications) and compare them to the claim language of their applications to see what the Examiner allowed and did not allow.
Journal of Intellectual Property Law & Practice (2013) 8(8):578-580. doi:10.1093/jiplp/jpt088.
Here is a ruling over a European patent in which broad claims were deemed enforceable:
Regeneron Pharmaceuticals Inc v Genentech Inc  EWCA Civ 93,
Court of Appeal (England and Wales), 21 February 2013.
This ruling confirms that a broad claim in a patent encompassing a
large number of unexemplified embodiments can be valid and
However, it is generally much easier to overturn a broad claim than a narrow claim. The larger the space an independent claim covers, the more susceptible it will be to challenges on Prior Art and non-enablement (not enough information in the specification to support the claim). If you are certain that there is enough white space (lack of Prior Art) around your independent claim, and that everything you are claiming is supported by your specification, then are probably safe to make the claim.
However, the Examiner is ultimately the one that you need to convince.