I'm going to say it's close to impossible for anyone to teach you to sing, but reasonable for someone to help you sing better. Start on your own. Second, anyone who sings period, even those not as good as you, can help you.
Here are some tips, though...
Can you match pitch? If so, just try singing single notes, you don't even have to know how to play piano, just hit one random key at a time try to sing the pitch. (A good place to start is the middle of the piano and go up if you're a female or down if you're a male.) Also, sing what you like. It's a lot easier to do something that you enjoy. I don't enjoy basketball, so I don't play/practice it. That doesn't mean I don't get any exercise whatsoever, though. I just do what I find enjoyable.
And, I'm going to say "no", you don't need a vocal teacher. I'd sung since I was (5, maybe?), and in tune, but didn't get a vocal teacher until I was 11.
3 bad habits to avoid would be: (don't worry too much, though... a lot of good singers do this)
Clearing your throat. It grinds your vocal folds together. (I'm guilty of that. 😞) Don't even think about it. It makes you want to. Also, don't sing way out of your comfortable range. Who isn't guilty of this? Many popular male singers (me too) sing way higher they probably should. Don't drink anything but water before, and don't eat anything sticky/sweet before. It makes it harder to sing and reduces your vocal range.
4 good habits would be:
If a song is too high: Use your resonant (so-called "head") voice. It can increase your range about a half octave. (6 semitones exactly, for me) If you have no idea what I mean by head voice, look it up. It's a bit hard to explain. The other option is to sing louder (but don't yell) if it is too high. My head voice is very weak, so I sing loud instead. Also, make your consonants clear. (I'm guilty of this one, too! 😄) If you sing into a mic, probably want to use the soft spongy covers for it if you get into this habit. That way you're s's won't make everyone cringe from the high pitch. Don't freak out if you suddenly sound terrible on one note. The closer you are to being on the correct note the worse it sounds, until our ears can't hear the difference. And warm up first. Even if that's singing a scale.
A habit I have is to make my voice sound like the singer. (Or sing with someone who sounds like you.) This makes it easier to sing in tune, since the sound waves match more accurately. I sound a lot like TobyMac (you probably don't) and I have a similar vocal range (mine's a little higher), so I sing his songs a lot.
In terms of memorization, think of a song in a simple sequence. If I were trying to memorize the pre-chorus of "Beyond Me", I would think "first stars, then water, then need, then see." I learn new songs in under a week this way. (And old songs in 24 hours on the high end.)
One last point, and this is a big one. In general, if you are doing anything for your own pleasure, keep in mind you don't have to be good. (Although I know how great the "being good" feels.) The only person you'd be in competition with is yourself and yourself past, and you'll always be better than your past as long as you keep practicing, just as good as your are now. Instead of saying, "Holy cow, I'm bad at this," say, "It was[...] not bad, but there's always some room for improvement." And no one better than you would say you're bad at something. If someone says you're not good, they're not any better than you at that or something else. And anything is possible.
P.S.: I'm a believer (I guess you could call me a "Jesus Freak") and I'm not a huge fan of hymns, so that might not be a great place to start.