Vicente, these are both pretty strong words to use if all you need is help with homework. Your usage of the words is correct, but no one would ever say that unless they were being sarcastic. You would beseech someone to save your daughter's life. Beseech is not used except in the gravest of situations. Pray is just slightly less grave. I pray for your safe return. I pray for world peace. You don't pray someone helps you with your homework - I guess unless, if you fail this class, you flunk out of college, return home a failure, are disowned by your family, and live an isolated desperate life as a pauper unless someone helps you with your homework.

I think - "I believe...", "I'm not sure, but..." "Possibly..." I want to - "I would like to..." "I'm ready to..." "May I..." Thank you - "I appreciate it (that)"

It is a very polite and formal answer. Not condescending at all. More informally you could say, I'd be happy to (help, assist, whatever). You don't have to say "help", it's implied when you say, "I'd be happy to".

And for the American version, they are called a curb or curbing. You might say "curbstone", but you'd spell it this way.

I feel (and it is a feeling, it's not exact) that not long ago and not so long ago are referring to less than a 100 years. Not long ago, women were unable to vote in the U.S. Not so long ago, women were unable to vote in the U.S. But it's all contextual. When have you last had a tetanus vaccine? Not long ago. In this instance the speaker means a few years or less. The "so" is an emphasis word and doesn't change the meaning

I think they are interchangeable in most situations. " Supposed to" might sound a bit colloquial, but it's commonly used. Let's make a deal, we'll use "should" in formal writing and either one informally.

This is an odd sentence construction - not wrong, just not as clear as it should be. in this case, "so" means "in order". If you move the "so" to after "placed" the sentence will be clearer Instruments have been devised and can be placed SO that all three elements can be recorded in different graphs.(the end) Instruments have been devised and can be placed IN ORDER that all three elements can be recorded in different graphs.(the end)

Traditional industry Internet industry Internet company Be careful not to put too many "n"s in internet. Two "n"s only, not three.