When you mention a solid product, I imagine you mean that you'd like to create a product that can satisfy the essential user needs, that are already being fulfilled by the competition.
Number of competitors
I think you should have enough competitors in your analysis to be able to form groups so that you can not only understand the characteristics of each group but also be able to compare them against each other. Having groups would help you better understand where'd you think your product could fit and where you wouldn't want to compete. Doing this without having groups is more complicated, as focusing on the features of a single competitor might cause us to miss the bigger picture.
How complex should it be?
I think it all depends on the strategic intent behind the analysis. How much do you need to know to have enough confidence to take the next step? How certain do you need to be? How will you achieve that level of confidence outside of competition analysis?
Identifying user loyalty and engagement
Now, this is a tricky one, but there are a few ways you could look into this.
A loyal user is less likely to churn or switch to the competition. If they are actively searching or getting information on alternatives, that means they might not be too loyal. Now, targetting those specific audiences is hard. Ideally, you'd have a list of current users of an app; it might be from a user group, or you created a survey and collected that data. If those aren't available, there are Twitter ads that allow you to target followers of competitors. Now, you can create a campaign that doesn't necessarily talk about your product but could be of value for someone comparing options within your industry. Once you have enough traffic, try to find a pattern, is there a specific group that had a higher engagement with your content? What parts were they interested in particular? The quality of the content you put out will determine the value of the data collected by the campaign, so make sure it does relate to the audience needs.
Being first in the market
Problems never change, and whatever problem your product is solving, will most probably have an existing solution, even if not optimal. The same methods will apply, as long as you understand the underlying needs and identify the set of solutions your potential users are relying on to fulfill their needs.