So, assume I have an iOS application with two components. Let us call those C1 and C2. C1 takes input from the user and does some calculations then stores it for C2 to do more calculations and display the results. I discussing a hypothetical example because I cannot discuss the invention. How would both of the components fit in a patent application. Both C1 and C2 are unique and non-obvious. C1 outputs data for C2 input. So, C2 is reliant on C1. C1 and C2 will be two aspects of the invention. Though, will C1 and C2 be regarded as a single method or two methods in this invention. Also, what if I want to protect both C1 and C2. Should I write C1 in independent claim 1 and C2 in independent claim 2.
You forgot a question:
"Can I protect both inventions in one patent?"
The answer to this question will answer a big chunk fo the rest too. The concept in question is called unity of invention. It exists in the PCT and the US and Europe and most other countries and it more or less says Two independent claims may only be granted in one patent if the underlying invention is the same. Normally this leads to the problem that the underlying invention has to be claimed.
In your case that means that C1 and C2 as a combination would be the underlying invention. So one of your independent claims should be C1 + C2. If you don't have that claim, chances are the examiner will say you are missing unity of invention and you'll have to decide to go for either C1 or C2 and file another patent application for the other one claiming priority (continuation, divisional, ...).
So the question isn't exactly
will C1 and C2 be regarded as a single method or two methods in this invention
as this can only be answered for the exact case and the correct answer will be determined (and defined) by the examiner. But if they are not, you will not get a patent containing both.
Also, what if I want to protect both C1 and C2. Should I write C1 in independent claim 1 and C2 in independent claim 2.
As is obvious from my explanations above, both should be contained in one claim to make sure the unity of invention is accepted. But of course you want to protect C1 and C2 independently. As long as the examiner thinks it is one invention, there is no problem with claiming C1 and C2 in separate independent claims too.
This leads you to having at least 3 independent claims, C1 + C2, C1 and C2. Leaving out the first might result in having to file another application, leaving out the second or third will result in narrowed protection. If you claim only C1 + C2, everyone is free to implement only C1 or C2.
For a discussion on how many separate but united inventions an application can have see Combining two claims for two inventions in one patent .
If each of C1 and C2 can stand alone (even if you don't see the value in it), they should be claimed as separate independent claims. This is because each is a separate invention.
One way to consider this would be whether C1 or C2 could be replaced with something else without it destroying the overall invention. That is, could you envision an alternative to C1 which would provide the input that C2 needs? If so, C2 probably is a separate invention (and vice versa). If you include both these in the same non-provisional application, you may receive a restriction requirement (termed a lack of unity objection in every non-US jurisdiction) when you do this (as explained by DonQuiKong), but that's remediable by paying fees.
Conversely, if each cannot stand alone, they should be claimed in combination only. This is because each of C1 and C2 alone would lack utility.
In a comment, you mentioned:
C1 is simply a new way to input data to a cell phone like watching the screen do some visuals and effects and corresponding to those. Then the result is used in C2 to actually display whats intended from the invention.
C1 stands alone (it is a method of input). C2 stands alone (it is a method of display, which ostensibly could receive data in any way). There might be a nice synergy by combining the two, but they aren't essential. In this case, they should be claimed as separate independent claims.