Hi SNM - congrats on your baby!
It's tough, the sleep thing, isn't it?
It sounds like her night-time sleep isn't too bad for her age - certainly, she does far longer stretches than my DD did at that stage (and indeed does at 9 months)
Re naps: yes, they can be tough. At that age, she may not be able to stay awake contentedly for more than 45mins at a time, so you could try putting her down to sleep before the sleepy signs start.
I'm afraid it's very common for babies at that age to refuse to be put down for naps. My DD would sleep when worn in a wrap sling and we also did loads of pram rocking which worked with patience. Do you have a sling? A Kari-Me or an Ergo would be worth considering (not a Baby Bjorn, they aren't very comfortable). You usually have to keep moving for the baby to sleep in them, but at least you have your hands free, so you can get a surprising amount of stuff done.
Also, have you tried a bouncy/rocking chair? Works brilliantly on some babies. Don't buy before you've tested out whether it works on yours, though! See if you can borrow one.
Don't worry about establishing a routine just yet - you'll soon find as you get to know your baby's needs that things will settle into a pattern that suit her. Trying to make them settle into a pattern that suits you can be too stressful, try to go with the flow.
Can someone else help for an hour or so every so often? Just to hold her while you have a bath, etc? Do you have any family, friends or DP who will cook for you (get a bunch of portioned out meals in the freezer - it's a godsend when you can't put the LO down).
Also, have you tried Dr Karp's 5S baby-soothing technique? Look it up on Youtube for details - especially the extract from Richard and Judy. It really does work.
And no, you're right not to let your LO cry herself to sleep. She's too tiny for that.
The good news is THIS TOO SHALL PASS!! My DD was very like yours, but eventually, she did allow me to put her down to nap - albeit in the pram (we've only just started tentatively using the cot...).
HTH!