I'm not on any social media, but found a good job. Probably the social media advice is sound, and you can pursue it, but also focus on just being very fast and accurate in technical interviews. Consider making an account on hackerrank (not linked to your main email, so recruiters don't find it) and doing the python and javascript Cracking the Coding Interview or other problem sets for just a couple days of study. This is a fast way to ramp up! This way you focus on actual technical skills, and not on your appearance (at meetups) or recruiter spam (linkedin).
Also, don't worry about companies or recruiters bad-mouthing you to one another. It rarely happens for legal reasons.
About phones:
For phone issues, consider using google voice on your laptop with a headset ($10) and fixed Google voice number instead- this will be hard when you're on the move (can forward calls), but it will make sure you can occasionally have high-quality phone calls. I almost never needed to accept or make non-scheduled phone calls during my job search. To sign up unfortunately you'll need at least temporary access to get a verification call on a mobile or landline (but hopefully the shelter or a public phone can help with this).
Depending on how big a volume of possessions you need to carry with you, scout out all the Starbucks (which now allow use of their wifi and bathrooms without purchase) in a reasonable distance, to find one or two with quiet corners where you could take an interview. If the interviewers hear sound in the background, tell them you're in a Starbucks. If they ask why, say your roommates are loud so you tend to work from Starbucks. There shouldn't be any further questions about that.
This fellow has been abandoned by a society and by a government that doesn't invest in its own people. It's not a law of nature that no one cares about him (OP's situation would be different in almost any other "developed" country) and what you call self-pity is a natural human reaction to misfortune.
Unfortunately, though, @jl2718 is right that many employers won't look upon OP's situation positively, and it's hard to tell if any will (except @leesalminen, who apparently will). Therefore some strategic non-disclosure of circumstances is advised.
Also, don't worry about companies or recruiters bad-mouthing you to one another. It rarely happens for legal reasons.
About phones:
For phone issues, consider using google voice on your laptop with a headset ($10) and fixed Google voice number instead- this will be hard when you're on the move (can forward calls), but it will make sure you can occasionally have high-quality phone calls. I almost never needed to accept or make non-scheduled phone calls during my job search. To sign up unfortunately you'll need at least temporary access to get a verification call on a mobile or landline (but hopefully the shelter or a public phone can help with this).
Depending on how big a volume of possessions you need to carry with you, scout out all the Starbucks (which now allow use of their wifi and bathrooms without purchase) in a reasonable distance, to find one or two with quiet corners where you could take an interview. If the interviewers hear sound in the background, tell them you're in a Starbucks. If they ask why, say your roommates are loud so you tend to work from Starbucks. There shouldn't be any further questions about that.