People have answered your questions regarding earning plat and trading (prime parts and warframe.market), but not really much else.

First, slots (and forma) are two of the main ways DE makes money, even from players who don't care for cosmetics. It's a F2P game, and in the grand scheme of things, slots and forma don't cost that much, and due to the trading between players, even those who spend no $ can earn plat and buy them (taking plat bought by someone else out of the economy). There are occasionally free slots (and forma) but not too many. At least a few purchased slots are essential to progressing far, if just for multiple frame or weapon options on certain missions.

Second - most weapons, especially the blueprints bought from the market, are "MR fodder". Meaning you build it, claim it, level it and then sell it off for credits, freeing the slot to build and level another. Many things other than weapons could be seen as MR fodder, too. Not sure how far into the game you are, but at the end you need only 1 kdrive or archwing, probably at most 5 different companions, and if you are really stingy, maybe only 10 warframes.

As someone who's leveled every item in the game (bar 3 I can farm, 1 that's a login reward I don't qualify for yet, plus also the 3 Founders items I can never have as I wasn't playing when the Founders packs were being sold), I can say that my ~ 125 weapon slots is too many. Most weapons I have kept I'll never use again, but I keep them, for the most part, because they were hard/time consuming to farm, so if I ever did want to use it, getting another would take time. There are like 600 weapons in the game, and only the die hard would have enough slots to keep one of each. But they would see my paltry 125 slots and just laugh.

As for frames, I'd recommend keeping one of each (base or prime), just in case. But every other type you can generally get rid of all but the one (or few) that you use regularly if being economical is your aim.