1-Counting there means that all the suns you have that wasn't converted will be changed as soon as you reach 25 excess suns total. For example, you got 440 suns, since the conversion ratio is 25:1, supposedly you should be receiving 17.6 strange stones. However, since decimal strange stones isn't a thing, that 15 suns (0.6*25) will be kept on hold until you get another 10 excess suns (10+15=25).

2-Yes.

3-Monday, 0500 server time.

4-Not necessarily. You can either save them in your mail and claim it on the next week or convert them to strange stones if you want to purchase something in the Mysterious Shop. As Kuro mentioned, best to cap it and save your excess suns as it does give extra power. I got a 680 power increase just by capping the suns if you're wondering.