Can I tap into this main gas line for my natural gas grill?
If your state has licensing laws a plumber can not work on this, you will need someone with a heating license. Most states with these laws have a system by which you can look up a persons license number and verify they are licensed and may even be able to find out if they have made any violations or scams.

I would suggest changing as many of those fittings with new as possible while you have it open. Some people will tell you that you can't use a street fitting or a bushing, in a few areas and canadia this is true, but for 99% of the us it's fine. If you're worried about the male threads cut in the cast fitting it's very easy to pipe it differently and I don't see you needing them here anyway. 

There are a couple important things though:
1-Pressure! Make sure the line is at the proper pressure for your grill, you will need a regulator, you might be able to use the one that came with your grill.

2-Gas type, if the grill is meant for propane and you give it natural gas which has a lower energy density it might not heat enough.

3-Drip leg, before the appliance, 99% of code requires a drip leg, a tee with a 3" or so nipple and cap pointing down, basically a dead end, it catches dirt, rust, whatever. Some guys argue they are dumb, I have seen exactly one drip leg with stuff in it, but it was a good amount, not worth the risk of clogging any thing in my opinion, just put one on.

4-In line with the drip leg issue, I wouldn't use ptfe tape, there are approved tapes but if a small piece tore of from the joint it's very light and could flutter down the pipe. Just use an approved pipe dope.