Caveat; not a native speaker. Hopefully one will come along and clarify or correct anything I get wrong.
The regular imperfective of to write is писать. The usual perfective is написать. However, you can use different prefixes to express different nuances. In this case, записать. But what if you want to use that meaning as an imperfective? писать won't work, and записать has to be perfective. So then a new imperfective needs to be formed from the new perfective verb, and that's what записывать is.
If it was perfective future it would be запишете.
flootzavut is correct. That was a good piece of advice.
Nuance or a slightly different meaning is what prefixes are often used for. For example, "записать" means to record or to write down. You write all kind of stuff for different reasons, but when you record (when you note it down), you do it to "store" the information—be it someone's words, a note to buy eggs and milk or audio of an actor's voice).
Now, since "to record" might be an action performed repeatedly or as a prolonged process, you would ideally want an imperfective verb for it. How inconvenient would it be if we made up thousands of new shiny verbs but could not use them half of the time! Thankfully, Russian often forms a secondary imperfective using some suffix. -Ива/-ыва is a very frequent and productive one (for example, E-conjugation verbs behaving like читать use it very easily).
I don't know. It seems odd that the main translation has neither "write down" nor "record". It might as well be a bug because I sure remember editing this sentence.
No. to copy would be списать (e. g. homework) or копировать (e. g. somebody's acts or behaviour, it's rarely used for notes, but you can use it to say "copy smth on printer")