I'm bBusy. I'm Busy.

I have've been (very) busy recently. I've been (very) busy recently.

I have been busy recently. I have been busy recently.

I have been busy recently. I have been busy recently.

I have been quite busy recently. I have been quite busy recently.

I have been busy recently. I have been busy recently.

Or: I've been busy lately. This version has more of a casual and natural feeling.

I couldn'twasn't able to study English and watchlook at/browse langconnect. I wasn't able to study English and look at/browse langconnect.

I couldn't study English and watch langconnect. I couldn't study English and watch langconnect.

"watch" is a slightly strange word here, you don't really "watch" a website, "watch" is more for films or tv shows or videos. Do you mean write journals on langconnect, or read submissions, or give corrections? Or maybe "keep an eye on", like, look at it from time to time to see if there are new submissions?

I couldn't study English and watch langconnparticipate in LangCorrect. I couldn't study English and participate in LangCorrect.

I couldn't study English and watch langconnpost entries in LangCorrect. I couldn't study English and post entries in LangCorrect.

I couldn't study English and watch lhaven't been able to study English or come onto Langconnrrect. I haven't been able to study English or come onto Langcorrect.

I changed the verb to the same tense as the last sentence. "use Langcorrect" = use the website's features (eg. write a post) "come onto Langcorrect" = open the website, maybe read posts or check notifications

I will be still busy but, I want to study it and watch here busy, however I want to study English and view this website as much as possible. I will still be busy, however I want to study English and view this website as much as possible.

I will be still be busy, but, I want to study it and watch here as much as possible. I will still be busy, but I want to study and watch here as much as possible.

I will be still be busy, but, I want to study it and watchparticipate here as much as possible. I will be still be busy, but I want to study and participate here as much as possible.

I will be stillEven though I’m busy but, I want to study it and watchish I could still study English and post here as much as possible. Even though I’m busy, I wish I could still study English and post here as much as possible.

I will bethink I'll still be busy in the near future, but, I want to study it and watchcome on here as much as possible. I think I'll still be busy in the near future, but I want to study and come on here as much as possible.

I changed the start of the sentence to have the full meaning of "これからも忙しいと思いますが".