Sounds like she's exploring, learning about her surroundings, and curious. Let her explore as long as she isn't hurting. If hurting, let her know it hurts...respond with "no" or "ow" and pull her away. Otherwise, talk soothingly as she explores, telling her what she is finding. If it's not forbidden, she will likely satisfy her curiosity and move forward to the next thing, getting past this grabby stage.
She's learning that she can affect her surroundings, how she and others fill space, about spacial relationships--more than intending to hurt or irritate. She's just 7 months old and there's a whole big world out there she is discovering!
Also, some kids like to be held more than others (and some parents like to be touched more than others). When held, it may be sensory overload. I'm not saying this from any well-researched standpoint, just my gut feeling. Just remember that each person is unique (child and adult) and has different needs and desires.
As for eating, can you give her finger food where she controls the speed with which she gets it to her mouth? Or can she handle a baby spoon with the kid grip on it? She may just want to have some control over that...or not. (Ask the day care how they handle feeding with her.) I remember the fun we had with cheerios and peas but I can't remember the age we started that. Our son is 12 now.)
If she's big enough for finger food, give her just a tiny bit at a time. If she eats that bit, then give her more. But don't give her the whole supply of food at once if she just makes a huge mess with it. It may just be a game to her. That being said, I don't think there is a parent who hasn't had to clean splattered food from the walls and crevices of a room more than once when their child was small.
Of course, it's important to know that there is also exploring going on with making the mess. Our son loved to explore the feeling of the different foods--some were soft, some gooey, some slimy, some squishy, some spongy, some scratchy, etc. With a large enough surface on the high chair, and a big lip to stop the food that isn't tossed, it is a veritable playground of textures. Let her explore.
I just took off my jewelry when our son was at his grabby stage. The temptation was removed. Or if I kept it on, I would say soothingly "gentle...gentle" and he eventually got the picture and had his curiosity satisfied.
One of my husband's favorite memories is holding our son so that they were facing each other. Our son would explore the buttons on my husband's shirt, sticking out his tongue in concentration. They could spend countless minutes like this. That memory is indelibly imprinted in my husband's memory banks.
As an aside...We were older parents that worked opposite shifts for years. It was wonderful! We each had quality time with our son that we remember fondly. Just remember to make time for yourselves as a family and a couple as well. It's hard when they're little but it will go a long way in bonding you as a family in later years. Enjoy!