1) The best split ratio for your cells really depends a lot on the cells you have. If there is any literature available elsewhere on the cell line you are using, you should probably start with that and go from there. Certainly anything you have from the place you sourced your cells from would be useful. In my experience, what works in one lab, does not necessarily work the same in another even though they would seem to be working in the same conditions.
I would start with a range of cells splits (eg. 1:5, 1:8, 1:10) and see how they like it. If they are confluent in 2 or 3 days, try a larger number (1:20). We aim to split our cells once a week, so we aim for a split ration that will accomodate that, will also keeping our cells alive and happy. Having said that, there are those that prefer to be split more often or require a certain cell ratio. That's where having specific information on our cell line would come in handy.
2) I was always taught to wash the cells twice with PBS. I find that your first rinse will be coloured by the media you are using, while the second rinse will be clear. I suppose that way you are ensuring you have got everything off.
3) Cells will often clump together after trypsinizing. They need to be broken up by aspirating carefully with a pipette or similar item once they have been resuspended.. This will normally not damage the cells. Some need more effort than others.
Hope that helps.