1998 Toyota Corolla starter problem

I started having problem to start the engine a couple of weeks ago. Some time I have to turn the key 2,3 time to start it. But when it starts it start fast. A technician told me I had to replace my starter, when I asked him (he has not run any test).

I was going to replace the starter, but before I decided to do this, I could not start my car any more. From what I read online, I most likely have a bad starter.

Her I have some other symptoms you help to to see if it's the starter or I have some other problem (in addition to this?).

I have just change the battery as well, brand new. Yesterday, when
I tried ti start engine, first I heard click, and then next I do not see any battery at all, when I turn the key, no light is on, no any sound when I turned the key. I took the battery to run a test. I was told battery was totally good.

I put battery back. First I tried to start engine, it has power, engine did not start, and then I did have battery again. I disconnect battery cable, and then reconnect. The same thing happens again.

Here is my questions
1) Do I have a bad starter, or some other bad electric components?
2) From what I read online, it's not difficult to replace the starter by myself. But some said, for 1998 corolla, the starter can be reach from top, some say it can not reach from underneath. Which is right?

Thanks for help,

Max