If you launch a product to a few different countries, does it make sense to do usability testing in all those different countries?

You can of course use analytics that will give you statistics, but will not answer "Why?". Gathering Customer Feedback is crucial and You have to be preprared for low response rates. For better understanding of Customers' interactions with Your site You can use tracking/heatmap solutions (i.e. Crazy Egg or Hotjar). But most important is to define goals and identify steps that lead to them - what do You expect Customer will do or act like? What needs to be done to acheive it? Then start monitor those steps, gather feedback, mae changes and see if this works looking at stats.

You're on the right track. I'm glad to see you getting the steps in the right order. WHO are potential users of your product? WHAT problem(s) will your app potentially be solving for them? HOW much do these potential users value the solution of these problems? Find your user group of people who would pay for a solution to a problem your app will solve. Get their input. I would do this through a couple stages...the first involving live talking, and the second usage of a basic version of the app once you and they have figured out what its purpose is.

Look on Google Communities for technology focused BETA testing groups... Look on Linkedin Groups for business focused potential testers... Look on Facebook Pages for people who like apps/companies like what you are trying to bring to market... That should get you started.

Are you talking about actual design mockups (PSD files etc) or just directional sketches that will help illustrate ideas you're having about how to improve the pages? If leaning more towards the former, I'd put yourself in a position to not need anyone else necessarily and just focus on creating wireframe mockups of the pages (no typography or finalization of icons/the skin of the page) and start with the blocking and tackling of each page. wireframing it also let's you more easily bifurcate between the web and mobile UX (if that is a part of what you've identified as an area that can be improved upon) - plus in my experience wireframes give you more of a blank canvas to start with while not narrowing your possible ideation phase with already in-place icons or imagery - basically it lets you work from the feet up each page. Taking this step (with wireframes first) allows you to revise and iterate on your ideas and THEN go find someone to produce mockups/design files in a more streamlined fashion (you dont want to be creating and constantly editing full design iterations as that would be a heavier, cumbersome and most costly process.) I've also found the narration process around wireframes much smoother and easier for inviting other contributors and capturing the commentary of the "why" to go with your "what". Good luck, feel free to reach out if you need any other suggestions or walk to talk through options!

UserTesting can be instructive in terms of understanding whether people understand your copy, CTAs, and intended flows but generally, I've found the quality of their panels to be pretty low. You're almost always getting people who are not your actual users, so the feedback can only be generally applied as above. I find whatever web analytics package or packages you're using are generally able to provide much better insights. I also really do believe in *real* user panels. Buying pizza or offering small financial incentives to real users to click through new flows where they are talking out loud or answering specific questions is going to give far more actionable insights than anything else. What I like to do is take my best guesses as to what's not working or what I'm looking to improve and then discover/validate via real in-person customer panels. Happy to talk through this in more detail with you in a call.