I would be more than gladvery happy to take the offer.

"More than glad" isn't a phrase very many native English speakers use, when we use the phrase "more than (BLANK)" to communicate that we are very pleased with something we usually put the word "happy" in that blank to make the phrase "more than happy," I will also say that this phrase ("more than happy") is usually used when we are communicating to somebody that we are willing to do something for them, for example "I would be more than happy to hang up your coat," or "I would be more than happy to buy you lunch today," basically when we want somebody to know that they are not inconveniencing us and that we want to do an act of service for them. The sentence is very polite as-is, but if you really wanted to boost the sentiment and make it very advanced you could say something like "I am very honored to receive this offer, and I will very gladly accept it." :)

I would be reallymore than happy to do itake care of that.

A more advanced structure here really depends on what "it" refers to and who you are saying this to. For example, if you are a customer service representative and a customer tells you about a problem, a great response would be "I would be more than happy to take care of this problem for you." The "for you" in this sentence comes off as though you are doing an act of service for somebody, and is probably best used when somebody is asking you to help them rather than telling you to do something the way a boss would. For example, if your boss assigns you a task at your job, you could say "I would be more than happy to do that."

Your sentence is still completely comprehensible and very polite, these are just a couple of ways to make the sentiment more personal and mimic native speaking patterns. Great job my friend!!!

I am interested in further information on the...

I have no correction on this phrase, I just wanted to let you know that this is the simplest and most clear way to communicate the idea represented by this sentence. If you really wanted to, you could say "I would be very interested in further information on the..." but it's completely a stylistic choice and depends on whether you think that goes better with the tone of what you are asking for! :)