I'm proud of/to/that ...

Dear native English speakers,
Would all the sentences below be used? If so, would all mean the same thing in each case?
1 (a) I'm proud of being a photographer.
(b) I'm proud to be a photographer.
(c) I'm proud that I'm a photographer.

2 (a) I'm proud of having won a gold medal.
(b) I'm proud to have won a gold medal.
(c) I'm proud that I won a gold medal.

Would all be used? If so, would all mean the same thing?
3 (a) I'm worried about my daughter staying at home alone.
(b) I'm worrying about my daughter staying at home alone.
(c) I'm worried that my daughter is staying at home alone.
(d) I'm worrying that my daughter is staying at home alone.
(e) I'm anxious about my daughter staying at home alone.
(f) I'm anxious for my daughter to be staying at home alone.

Thanks in advance.
Hirashin

For 1 and 2 all would be used and have the same meaning.
For number 3 there is a difference between worrying and worried in this case. Worried could mean that it hasn't happened yet and you are worrying in advance at what might happen. While worrying sounds more like she is currently staying home alone and that the worry is a current and ongoing thing. Anxious can also vary from the meaning of worrying/worried. In context like this it could mean you are looking forward to the event with anticipation. With (e) it wouldn't be likely you mean you're anticipating it but (f) seems odd to me. It seems more like you would be looking forward to the event. Not sure if it's grammatically correct. I feel it needs a grammatical correction but not sure how I would correct it while retaining the meaning.

Thank you for the help, OoTmaster.

How about (b') and (d')? Would they be used?
(b') I worry about my daughter staying at home alone.
(d') I worry that my daughter is staying at home alone.

Does "anxious" in (e) mean "anticipating"? Then, in which case would the word mean "worried"? How about (g)? What would "anxious" mean in it?

(g) I'm anxious about going abroad.

Yes (b') and (d') would both be used. In (e) anxious can mean anticipating but with a negative connotation. Normally anxious is either positive or negative depending on context of what it's referring to. So since it's likely you're not looking forward to your daughter staying at home alone then it comes off as being worried. If we had context to think you would want your daughter to stay home alone it could carry a positive meaning. For example, when I visited Japan I told my friends/family that I was anxious about my trip to Japan. I was eagerly looking forward to my trip to Japan since it was a vacation it's assumed to take a positive note there. Now if Japan had something negative going on recently anxious would more likely be negative. If there were riots in Japan in the place I was going, then "I'm anxious about going to Japan" would likely hold negative meaning.

How do (b') and (d') differ in meaning from (b) and (d)?

Is it that (g) has either a positive or negative meaning?

How about this? Would it only have a negative meaning?
(h) My grandmother is anxious about my/me getting injured.
Would it be the same as (i)?
(i) My grandmother is worried about my/me getting injured.

There might be only a small difference between (b')(d') and (b)(d).

(g) could be either positive or negative. Reading it as is without context I assume it to be positive.

Yes (h) would only be a negative meaning. I would say there's a difference between (h) and (i) but it's slightly nuance. Anxious is mostly linked with anxiety while worry isn't always associated with anxiety.

If you were to say "My grandmother is anxious to see me get out of the hospital after getting injured." it would have a positive meaning while worried/worrying would have a negative one. Such as she might be concerned how you will get back to your daily life after recovering from your injury.

"I'm worrying" is about how you're feeling right now.. "I worry" is just a general statement and usually just means that you have that feeling sometimes.

I'd like to note that realistically, B and D are very situational, as in it's almost never useful to point out that it's right now that you worry about something. The only use-case I can imagine is explanatory, e.g. if someone asks you why you're shaking. Even then, "worried" is more common.

Anxious and worry are fine as synonyms
Anxious has a Latin root meaning choke or seize up - as in a panic attack
Worry from Anglo Saxon root meaning to pull at something
(We still refer to worrying at a knot when used in a different context )