Is there any convention as to how many and how to choose the datasets?

No, this is entirely up to you and the details of your project.

The datasets should all be of the same study type (microarray/RNA-seq/etc.), right? But do the platforms also need to be the same? Can I use datasets that belong to different platforms (analyzing them each separately on GEO2R)?

As for your specific questions, you hopefully will never put them into the same quantitative analysis, so better go to some meta-analysis approach for which platforms and all can be entirely different. It's about finding common trends.

Can the sample source tissue/cells be different in each dataset?

Depends on your analysis and the underlying biology, no general answer.

How do you know how many datasets to use? Would one for each disease suffice?

Same as above, depends on what you do.

Please understand that biostars is great for technical questions and advise, not so much for figuring out the basics of how to start your poject since nobody here knows the details (if even present) of it. Discuss with your PI and peers what you want to analyze and then see what you need to achieve that. Be sure not to wildly combine datasets and think about defining a clear aim.