As a first note, the motivation for all of the following is that technical writing needs to be clear and easy to read. If your reader has to work to figure out what you're saying, then he/she is likely to not bother to figure it out, and stop reading instead. Your goal in writing should be to write clearly in easy to read prose so that the reader will read and understand what you have written.
And remember: much of what follows is my opinion. Your supervisor may have a different opinion (especially on the passive voice issue). Discuss things with your supervisor before you get too far.
Consider the following:
An example should clarify this:
Note that a "which" clause is parenthetical, meaning that it should be contained in commas or parentheses. To determine which to use, see if the sentence changes meaning when you strike the "that/which" clause. If it does, then you should use "that", otherwise you should use "which". Native speakers have a special neural net that gives them another test: Try both "which" and "that" in the sentence, and if both work, then use "that".
Just to complicate things further, the above only refers to one use of "which" and "that". There are other uses of both words (such as with prepositions like "of which", "by which", etc.) for which the above rule is irrelevant.
If you try writing without "I", you quickly find you (a) must use the passive voice, and (b) your writing sounds as dead as the dinosaurs. It turns out that there is an additional problem with completely removing the pronoun "I": it makes your writing unclear and difficult to understand. In particular, if you write "10 subjects were given the test and...". The question arises: Who gave the subjects this test? Who did this work? That's the curse of the passive voice - it doesn't tell you who the actor is.
One feeble attempt to solve this is to use "we" everywhere that you would use "I". Sometimes, of course, the use of "we" is correct: it may mean the author and the reader, or there may be co-authors. But when "we" replaces "I", it becomes a "royal we," referring to the writer and god (which was probably not the intention of the writer). The "royal we" is probably best left for the exclusive use of Kings who have been dead for centuries.
Further, in a thesis, the use of "we" is strange. This is suppose to be the work of the graduate student, not the work of a committee. Yes, a thesis is often the work of both the student and the supervisor, but usually the supervisor's role is just supervisory, with a bit of guidance and help when needed. Most supervisors are happy to have the student take credit for the work in the thesis (in return for co-authorship on the corresponding paper, of course :-).
So that brings us back to using "I" in technical writing. Again, note that the use of "I" is usually clearer and more objective. The last one may be a bit of a surprise, but if you voice an opinion in your thesis, it is critical to make it clear that this is your opinion (anyone using "the author" to refer to themself is referring to themself in the third person, a definite writing no-no).
The trick in techinical writing is determining when to use "I" and when to use another construction. When in doubt, ask yourself how important it is to both the clarity and to claiming appropriate credit for your work. The thesis is your work, after all, and you should make it clear what your contribution to the work is.w/
In any case, you should not use contractions in technical writing.