Okay getting onto the next part of my post (sorry for the delay!)
On saying no - I try to avoid saying "No" and use a more specific word. I use "Careful" a lot (And DS now says "Erful, Mummy!" which I think is cute), the old standby "Hot!" for drinks etc, or something like "On the paper!" if I see him drawing on a table, as he did earlier today (he ignored me even after I offered him paper, so I took the pen away in the end)
Actually this is a good example to illustrate another point - DS was upset when I took the pen away. But still, I don't see it as a punishment. It was a necessary step for damage limitation. The difference between this and a punishment is that it wasn't intended purely to be an unpleasant consequence. If he'd have shrugged and gone off to play with his cars or something I wouldn't have thought "Oh no, I'd better do something else, that clearly had no effect." But equally you shouldn't be afraid to do something which will upset your child, because sometimes it is necessary. (I haven't finished reading UP yet but so far this is the bit I feel he isn't very clear on.) You can do it in a respectful way (give a warning, ask for the pen, count to three, etc) and you should explain and you can apologise "Sorry DS, I know you want to draw, but we don't draw on the furniture." or validate feelings, especially if they are very upset, "I know it's hard when you can't have something that you want"
The other big thing is working out why you think they are doing something and instead of just dealing with the behaviour try to solve the root cause. Aggression or violence for example is often caused by stress or frustration, and removing the cause of stress or frustration is not always possible, so you need to show them an appropriate way to deal with those feelings, like drawing a picture, saying it with words, throwing beanbags (or maybe teddies?) at a wall, just arbitrary suggestions and obviously what is appropriate will depend on the age of the child, but it is a starting point.
Related to this is if they can't do one thing, e.g. climbing on a chair, can you provide something which it is safe to climb on? Actually if the wicker chair was that small I'd be tempted to let them climb on it anyway, they wouldn't be seriously hurt from a fall, and babies are actually quite good at testing their own limits if you give them a chance to. Dining chairs are more of a worry though! The only thing you can really do with this is to always supervise her around such dangers, field her away from them as much as possible, and then just ask verbally once or count to three and after this one verbal instruction/counting, pick her up and move her off it, as many times as it takes, or remove the chair completely until she is old enough to understand it, if it's at all practical.
But generally I let DS explore more than other people tend to let their children. I have stairgates and wouldn't let him do anything ridiculously dangerous like play near an open window he can reach, I don't have that much faith in his protective instincts! But let them fall to an extent and experience gravity, let them manage small steps etc by themselves, and if they DO have an accident don't whisk them away if they want to go back to doing the same thing. I used to do this with DS and I noticed that he would avoid that situation for a while and then suddenly go back to it one day and hurt himself again, whereas when I let him go straight back and try again he was really cautious, testing his limits etc, before making a step or whatever, and he'd work out how far he could go and from then was more confident on that particular climbing frame or whatever and much less likely to injure himself.
Lastly it's worth reading a bit about child development and being sure that what you are asking/expecting is age appropriate. For example, the overriding cry you will hear at toddler groups all over the country is "Share!" but actually, the average 1, 2 or 3 year old still engages only in parallel play (ie playing alongside rather than with other children) and the concept of sharing is alien to them. If they are playing with a toy they don't expect half of it to be messed around with by another child and they find it hard to deal with if this does happen, usually ending with fighting between the children, snatching the toy away or upending the whole thing on the floor. Taking turns is much easier for such a young child to understand. At 1 not so much (though you can certainly start showing them) but certainly at 2 or 3, if you go through: "Sally's turn; wait Daniel, well done Sally! Okay, Daniel's turn... good, Sally's turn..." etc etc, most of the time they pick it up fairly quickly. Surprisingly enough even the most "selfish" children seem to react well to this. It's like you've suddenly explained it to them in a way they can understand. Sometimes DS has a wobble when he wants to have the first turn and I make him wait but he soon comes round.
My head hurts now so I hope that some of that makes sense! :)