I've seen you on BYC. Welcome to this site. I'm still fairly new on here also.
1)How do differentiate between weeds and your plants when things first start growing?
I had that problem with celery last year. One weed we have looks a lot like celery. I don't have a simple answer for you other than for you to trust yourself. You already have a lot of knowledge on what the leaves look like from the grocery store or from looking at flowers. And different seeds behave differently.
With some seeds, like beans, the bean itself comes out of the ground when it sprouts, splits and looks like the first two leaves on the plant. Most aren't that obvious, but some are easy.
Many vegetables just look different from weeds. You'll quickly learn the look. Many are larger, like squash or gourds. Not tougher as they look vulnerable to me, but definitely larger. If you plant 3 feet of radishes, then 5 feet of carrots, you'll see 3 feet of one type plant then 5 feet of another type plant. You can make some pretty good guesses from this. When I sow seeds or even put started seedlings in, I put a small marker, usually a small stake of scrap wood with magic marker writing, at each end of the planting to tell me variety. That can help.
Some can look similar to weeds, especially if it is the first time you've grown it. Celery for me. Corn can look a lot like some grasses. For those you are not sure of, I advise patience. It will become obvious. There is a plant identification section on this forum. People are as friendly and helpful here as on BYC. Got a camera?
2)How do you know when your "below grounders" are ready to harvest (i.e. carrots,radishes,onions etc).
You can look at the days to maturity on the seed packet, but that is just a guideline when to start looking. Those seem to be from germination, not planting, and assume ideal growing conditions. Mine don't always get ideal growing conditions, but it tells you a "no earlier than" date.
Some, like radishes, will be pretty obvious. They actually partially mature above the ground so you can see when they are ready. With some, like onions, the tops die back when they are ready to harvest for storage. Of course, I use a lot of green onions so I take those when I am ready. And you can eat onions before the top dies back. At least I do. For some, like carrots and potatoes, you just have to start groveling in the ground to check.
For some of the in-ground crops, like onions, it is recommended that you remove the soil around the tops of the bulbs so they will grow larger. Obviously you can see when they are big enough. Some like potatoes would sunburn if you remove the dirt, so you can't do that for all of them.
You'll just have to learn about the individual crops. As you are aware, there are threads on here on most of them and search works as it does on BYC. It is a learning curve but don't be afraid to trust yourself. Most of the time it will be pretty obvious.
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