Hi, it is tough when they get to the point of needing someone near them all the time. It is a phase that will come and go right through to the toddler years. The best way is to help her through it as best as possible and not to try and make her be alone (yep, it's trying). It's fine to work on short moments away to get her used to the fact that you will come back (she's probably just getting aware of object permanence which where prior to this they don't realise that when you go away that you'll come back). Play peek-a-boo games behind a door or wall, and while things are positive stand behind the wall and talk to her and reappear before she gets distressed and gradually build up the amount of time that you're away but while she's ok with it if that makes sense. As far as getting more food for her, it's ok if she crys while you're getting more food, just tell her what you're doing and reassure her and try not to take it personally that she's crying, I'd probably just start to take as much food with me to the table so you're not put in that position if possible. Has she started on any sort of finger food yet, if not maybe a sippy cup to play with? Something on the tray works well for my dd.
As far as playing, I'd work on the peek-a-boo games but also take her around the house with you while you do chores and place her down nearby or whatever. If she's getting bored make sure you rotate toys and or scenery every 10mins, don't feel you need to play with her the whole time, sit back and read a book nearby, then warn her you're going to do something and pop out and back again.
That's all I can think of for now, but HTH
