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I would investigate the alternator and its wiring. There's a good chance your brushes are worn, and a new set with regulator will set you back about $35. Check fcpgroton.com. Meanwhile, put your battery on the charger... so you don't fry your alternator when it's back up and running. Removing the alternator is an easy 3-bolt affair... just disconnect the battery first.
The loose steering could be from a number of things, none of which is terribly expensive. Loose wheel bearings, worn ball joints or tie rod ends could all contribute. The Haynes manual will tell you how to adjust wheel bearings. Ball joints are about $17 a side, tie rod ends about $10 each. Replacement is probably Skill Level 1.7 - you'll need a jack and jack stands, but nothing more complex than metic wrenches and sockets. However, you probably should plan on a fresh alignment after changing those out.
Beyond those things, loose steering could also be caused by low tire pressure (you should have at least 28 psi all around; 30-32 is better), or a heavy load in the trunk. A couple of ticks up the complexity scale are suspension bushings; the rear A-arm bushings *might* give you a loose steering feel, but that's usually felt more at parking lot speeds.
Nothing you've describes sounds prohibitively expensive... with help you should be able to put off having to buy another car for a while. Keep asking questions here on the Board, and we'll try to keep you rolling.
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