AFAIK it wouldn't make any difference to the blood in your womb as it is a lining that is shed, it isn't like the fresh blood in your veins. The blood in your veins would thin but given that the lining of your womb is made up of older blood it would have already have been produced and deposited before you started your course of asprin.
how exactly? There is a finite amount of sponge to be got rid of from your uterus, nothng will cause it to be shed prematuerly. I wouldn't be willing to lose a day or two's bleeding at the expense of my general health.
What do you mean by "only aspirin". It is a drug with plenty of side effects. Just because it is widely available and does not mean that you should abuse it and take it when you don't need to. see here.
Funnily enough I had all sorts of problems with heavy periods and consultant said don't use aspirin for pain relief it will increase the flow! I was really surprised - like others I had always thought it was a finite amount but he said not. And he's a gynaecologist so I guess he would know.