Sounds like a lot of normal 2 yo stuff. Definitely have her evaluated if you are at all concerned. There is no harm in that at all! Absolutely if she feels she can't communicate with you and be understood that can add to her behavior problems.
I think if you have a hard time keeping yourself from yelling at her, it makes sense that she will scream in your faces. "Enough" definitely sounds like channeling what she has heard (I'm not judging here, we all lose our cool). A technique that is working for me right now (saw it recommended on a thread somewhere) is when you feel like yelling to whisper instead. I have found this instantly changes the dynamic and gets her attention. I don't mean whisper in a threatening way or anything. Just whisper. It keeps you cool and then she won't escalate (hopefully). I find if I lose my cool with DD she automatically escalates to meet or exceed me there.
I personally don't use time out. If DD is crazed or whatever, we will take a breather together to regroup but I don't think a quick punishing time out will have much effect. If the goal is to get her to cooperate, you may try to remove both of you to try to calm yourselves rather than fighting to keep her in a punitive time out while you ignore her. Also ask yourself if it is a case of tiredness, hunger or overstimulation. Sometimes we create a situation where it is impossible for them to behave, we set them up for failure. It may be that you can't go to Target with her.
My DD often doesn't want to do the organized gym activities (she just turned 3). I don't think forcing it is effective. I want her to enjoy the class and feel that maybe some of these things are just intimidating to her or something. I don't let her run around or play with other things, tho. If she doesn't want to do what they are doing she has the option of sitting with me and watching.
Hand holding is just not an option. DD does fight us on it sometimes, but there is no option. She must hold my hand. End of discussion, no wavering. When she was younger if she didn't want to hold hands she had a choice hold hands or go in the sling so she is used to the rule. Of course she does try to test it but then I hold tighter and the message gets to her.
I think the pickiness and not eating is an issue for a lot of kids her age. I follow the advice of "it's my job to offer good foods and hers to choose whether and what to eat." I try to have at least 1 food she will eat at all meals/snacks but if she doesn't want to eat, that's her choice. I am sure you can find a lot of advice on that from other moms who have been there. Food is one of the few things they have complete control over, so it is best to try to avoid making that a battle to fight as it will be a long one. Also if she will only eat certain foods, those may be foods she has an intolerance to and that can effect behavior. So maybe that's something to look into.
Since she has given up her nap she may be sleep deprived. Is she getting enough sleep? I know my DD gets wilder and less agreeable when she is tired and at that age they still really need a lot of sleep. So tho she has dropped her nap, she may need that time added into her night of sleep.
Try to give yourself a break. Some kids are more strong willed. It doesn't mean they are bad kids or that they need to be forced to be different or that they have ineffective parents. 2.5 is still quite a baby. They need a lot of help. Try not to worry about what others might be thinking when she is out of control. Yeah, right I know! But the fact is kids wig out, and some more than others.