It’s not difficult to learn to swim, but it can be hard to learn to swim good and have it do any thing for weight loss. You will have to learn to swim on top of the water though as you will not be able to do much under water.
I would also say to stay away from the breast stroke with a bad knee. I have one right now and this morning doing the breast really hurt, so much so that I switched to butterfly. I’d also not push too hard off the walls and even if you see others doing flip turns I’d avoid it because of your back. You’re not going to gain anything by doing flip turns for what you want.
As for breathing, you do not pick up you head to breath, you actually rotate your body. Of course you will have to turn your head a bit, but the rotation is what allows you to get your face out of the water enough to breath. You will want to breath out underwater so that you don’t try and do both too quickly.
You might want to check out a pull bouy. Basically it’s to keep your legs from sinking when you do pull sets, but for you it will help keep your body level in the water. The more your legs sink the harder it is to swim properly.
The goggles can be a bit pricy, but I think you can find them for around $20. I tried a pair and didn’t like them, but they were also dark and I like clear, and a bit too strong for me. My eyes are something like -1 and -1.25, I believe they only make them starting around -/+2. I think I still have my -2 around if you want and I can send them to you as I don’t like them. If I need to see in the pool I just wear contacts. The goggles will keep most of the water out, and even when I played water polo I didn’t have a problem with the water.
Weight loss can be a problem, not because swimming isn’t good for it, as many people say, but because people are not swimming hard enough. You will want to keep your heart rate up and keep moving. Whenever I go and swim in a public pool everyone is so slow and just playing around. It would be like saying I’m going to run to lose weight but really just walk for a bit. Also people tend to get hungry after swimming, either don’t eat, or eat some fruit, not a full meal.
I’d also suggest joining a US Masters swim team Don’t worry, it’s not a team like you think and they take a full range of swimmers. They will help you with your stroke and make sure you actually have a good workout. You will not have to swim at meets, though they are fun, it’s just a bunch of adults that like to swim.