Mouldy starter

I began making sourdough bread perhaps a month ago after many years of seeing it in my bread book.

I followed a beginners guide from this site and spent a week making my starter. Then I started making breads (a couple from here so far and one that was made in a bread machine), taking the starter out and adding 100g of water and 100g of flour. As I only have time at the weekend to make a sourdough bread, I put the starter in the fridge, getting it out at the end of the week to feed it again, before using it the next day to make a bread.

All was working well but then I was away for a weekend so I left it in the fridge for two weeks. I got it out last night and it had gone mouldy - both on the sides of the jar and a spot on top of the starter. From what I'd read, it seemed fine to leave the starter until needed again (within reason obviously, but two weeks seemed OK),

I decided that if I took off the top of the starter and took some of what was underneath that would probably be OK, refreshing with new water and flour just like I was. So I have done that. Is that OK?

But, the starter consistency had changed - the top had solidified more than it had previously (what was underneath was still more liquid).

Why did it go mouldy?

I read about scraping anything on the sides of the jar down, but that doesn't seem practical - it's always sticky and can't be cleanly scraped off the jar sides!

Is may jar too big - it only fills it about 10% of the way up the jar?

Should I be taking a small amount of starter and refreshing it in a new jar from time to time (maybe each week)? That way the jar could be clean and only have a little bit of starter plus new water/flour. That's sort of what I've done now - used a (clean) beer glass covered with cling film until the mouldy glass has been washed up.