Sawfly don't do more than cosmetic damage and can be ignored. The rose will grow more leaves if they're needed.
My horticulture teacher also ran a nursery and I asked her once what she did about things like sawfly or aphids and she said 'Nothing, I ignore them' and she just waited for them to go away, which they eventually did. All the plants there certainly looked to be in rude good health. She said the main thing is to feed, water and prune, but otherwise leave things be and let the local ecosystem find the balance. The more plants, the more insects, many of them beneficial. The birds help too and sparrows are excellent at cleaning roses of aphids and parasitic wasps, ladybirds and lacewings make short work of other pests.
Suckers generally have paler leaves and stems than the grafted variety and fewer thorns. Twist them off at the base rather than cutting, as this will make it less likely they'll regrow, then wait and hope for the best. Roses are pretty tough customers and aren't easy to destroy. It's only really if the graft union fails that they die.
Black spot has been an issue with this wet year. At work I'll use a fungicide but at home I just remove and bin the leaves and clear away any that fall.