How can I make an application to be opened at a certain time, on certain days.

The common way to do thid is to have a small AppleScript application running in the background with an “on idle” statement. This checks the time (ticks, date, and so on). At the right moment it launch the application you need. It is very simple to make this type of applications. There is also the iSchedule application making a similar work.

I know this is not an applescript solution but it sounds like a jog for Cron - this is a shareware package that will open an application or whatever whenever you have the need. check it out, you should be able to find it on one of the shareware sites. I believe it’s freeware.
Hope this is a help,