Weclome to Dominion Online!
1) Main point: Rated games do *not* respect familiar cards. The basic thinking is that it takes skill to be able to deal with 300 different cards in any combination, so if you are 'only' playing with a small subset of cards or concepts (like no Events, or no VP gaining, etc.), this isn't a true measure of 'Dominion skill', which the rating is supposed to measure.
2) If you want to play with players respecting your familiar cards, you need to play unrated games. The easiest to do that without setting up a table is to go the "Matching" tab, the click "Advanced Options".
Among the options there are "Rated Game" and "Practice Game". Uncheck "Rated Game" and check "Practice Game" (doing the former should automatically do the latter). If you then click "Start Search", you will be playing (unrated) games that respect your familiar card settings.
3)If you resign a rated game when all player are there (basically the moment you see the kingdom and your starting deck), this will be a loss and affecting your rating.
Again, welcome to Dominion Online, if you have any questions, feel free to ask.