I don't think you are rushing things, but I do think that you should just give her a spoon and if she uses her fingers then so be it, table manners come later. When they are learning to eat, be prepared for loads of mess. As the weather is a little warmer I usually take Alex's top off and put one of those bibs which have sleeves and she can make as much mess as she likes. I did the same thing with DS and he soon got better and I never have had any eating fads or picky eating with him. I think that food should be enjoyed any way they like! As for a fork, try steamed vegetables cut small (quite soft carrots,brocolli,cauliflower,courgettes (zucchini I think to some) I look after a 1 year old who only has his two bottom teeth but still refuses to let me feed him (he sees Alex enjoying herself so much) but that's what I give him to eat. Be on your guard, as obvoiusly chewing is limited, so be prepared to help them in case of choking, but this gets less and less the more they try it. He hardly ever chokes now, althouh he did pinch Alex's biscuit the other day and that got stuck, I think it was too hard for him with so few teeth, I didn't even realise he had it, you have to have eyes in the back of your head!
As for the sippy cup, My ds would bring his to me until he was about 18 months old. I think he was lazy. Your dd should be able to start this now, try to get her to do it herself. Try putting her hand to it and if you can get here to grasp it, then let go. I don't know many tips, Nathan was slow, Alex just did it, I didn't have a problem, with her. Hope this helps, and good luck.