In answer to your questions:
1) Yes. All Vita games are available as digital download. Beyond that, you can also buy many digital only Vita games, PSP games, Mini's, PS1 classics, etc...
2) There is no internal memory for storing downloads and save files on your Vita, so the memory card is essential for using the system. As for migrating from a 4GB card to a larger size. Yes, but it can be a tedious task (see below).
You can perform a migration primarily by three methods at this time.
1) Install the Sony Content Manager on your home computer, connect the Vita via USB or WiFi and backup the old card, then restore it to the new card (I believe there are a few games that are flagged to block backup, for these you will simply need to re-download them).
2) Use a PS3 for backup/restore (same issues as above).
3) With PS+ membership you can backup some data to cloud storage from which you can restore to the new card and then re-download all your games.
The 1st of these three options (using USB) is probably the simplest from my experience but YMWV. There is no such thing as a card reader for Vita memory cards and no indication that Sony will ever accommodate such an offering. So you cannot simply copy the contents of one card to another as you could in the past with the PSP.
If you only plan to only play cartridge games, a 4GB card will suffice. If you look to start purchasing digital content or subscribe to a PlayStation+ membership, then the regular free offerings will quickly exceed 4GB card (eg, WipeOut 2048, Uncharted and Gravity Rush combined will not fit on the 4GB card). In this later case just skip straight to a 32GB card and save yourself some headaches.
Even with the 32GB card you will eventually find yourself running tight on space if you accumulate more than a few major titles. That said, I suggest you jump straight to a 32GB card and setup content manager for backing up/off-loading any games once you near capacity. It is often quicker to restore them this way than by downloading them again since you don't have to deal with the system going to sleep and pausing the download.