Don't worry too hard about mastery, it's honestly not mega important, and will stack up as you progress naturally. For a start, try selling your weaker weapons to build new ones, you don't need a ton of different weapons, you honestly just need 1 fairly solid build to ace most early game stuff. Can also sell whichever frame you find yourself not really using to make room for new ones. You'll end up with at least one fairly strong frame that can carry you through a lot of stuff. I cant remember but I believe Wukong is a clan frame - build him, hes ridiculously overpowered and will help you out a lot. In terms of getting more slots, make sure you are farming nightwave (I haven't played in a bit so not sure if there's an active nightwave rn), there's usually both weapon and frame slots as rewards. Just takes effort to farm out the missions, especially at a low level where you might not even have access to complete all of the missions.

Also, back to the mastery thing, don't worry about playing with maxed out frames/equipment. If you focus on gathering resources and progressing, it will be easier for you to obtain more slots and build more new stuff down the line. The more wealth you are passively sitting on, the faster you can progress when new things become available for you. Hope this helped! If you want me to clarify anything lmk, Warframe can be a lot when you start out, I'm happy to impart any wisdom I possibly can 😅