Word Choice – Usage of ‘From’ and ‘Since’

1b) and 2b) are correct.

You could correct 1a) as:

He has been working under my direct supervision since two years ago.

and 2a):

He has not met her since long ago.

Since as used here points to a specific time, not a time span as in your examples.
See the definition since senses 4 and 5.

Let's get the easier question out of the way first. When you are confused, you can use about or on, but I think about is the "safer" choice. Behold the ngram.

As for for the taking, let's say that you need a job, and I own a business. I might tell you:

I have a job opening. It's yours for the taking.

or:

I have a job opening. It's there for the taking.

Basically I'm telling you that you could get a job with me, if that option sounds good to you. I could easily substitute "if you want it" for "for the taking".

Looking at the ngram, we see that common ways to use the phrase include

• there for the taking
• free for the taking
• [possessive pronoun] for the taking (i.e., his for the taking, yours for the taking, etc.)

I won't say those are the ONLY way the phrase can be used, but an answer can't delve into every possible usage of a phrase. Those three are a good start.

There's also a relatively high number of

• compensation for the taking

but those come mostly from legal documents; that's not a wording generally heard in everyday conversation.