Kawa Z650 Help Assuming Carb Problems...

Guud Day folks.
To start off, I am not extremely experienced with motor mechanics at all, but love to learn all the time. The thing is, I usually want to do it myself. I dont want to take it to a workshop and have things repaired by qualified okes and I dont want to ask a mate to look at and repair/adjust/modify. I want to DO IT MYSELF.
Now, just bought this old girl: (Dont know how to insert my pics on this forum yet)
The day i got her, she was going fine. Not 100% if I opened her up, but I was assuming that she needs some TLC, some fine carb adjustment, new spark plugs etc.
The next day, I took her out on the open roads with my friend. We rode the whole day, but at approx 5pm in the afternoon, she started to cut out, almost seemed to me as if she was running out of fuel. This could not have been possible, I thought, as I filled up the tank just before heading out the rather deolate, winding stretches of road along side the ocean.
So, I thought the petcock was blocked up. Eventually found a little pud with a guy that had some tools. Stripped off the petcock to clean the inside tank filter, but alas, the filter was clean.
Went on like this for quite a while. Eventually I got to a gas station and filled her up again. Immediately saw that the fuel just runs straight out again from overflow pipe on Carburetor No.2. I jumped on and rode her home, knowing now that I was actually running out of fuel the whole day en that float levels/stuck float bowel would probably be the problem.
Next day I took the carbs off. Adjusted and cleaned a bit with my limited knowledge, interweb and haynes manual.
Seemed to have fixed the problem of the petrol flowing out of the no.2 Carb. Took it for two short test drives and everything was fine again.
the next morning, I wanted to ride her all the way to work. It was raining, so I thought it would be a good test for the old girl, as I believe that water and older bikes tend to not go very well together. About 2km from my house, in the rain, she died. I pushed her all the way to a biker pub in the area and left her there untill I could return after work to check her out.
She stood in the drizzling rain that whole day. I took a bike mechanic with me and he could also not get her to start. Eventually I asked a random home owner if I could just get her his garage, just to be able to work a bit dryer. Eventually, after drying, cleaning, reconnecting, sealing, spraying, trying to start, she started and I could just just get her home, while running very rough.
The day after, I started to investigate a bit further, learning about the coils etc. I clenaed the areas where the points are, put new gasket and sealer. She started easily by this time, but was still missing quite badly. Then only, I replaced the spark plugs and she was perfect again. Again, rode her the whole day last Saturday and towards the end of my trip, once again she started to idle/rev rough and now she is standing again, parked. Starts immediatly, but misses like crazy. The spark plugs are black and smell like petrol. I cleaned them with sand paper, put them back and she seems to be missing even more than before I cleaned them.
I understand that this is a mounth full and I understand that there might bemany different probelms, but if you guys are kind enough to share some of your experience in this dept., I will take your advice and tick off things to be done to the old bird one by one, untill she can purrr across many miles of open roads.
To start off, I am not extremely experienced with motor mechanics at all, but love to learn all the time. The thing is, I usually want to do it myself. I dont want to take it to a workshop and have things repaired by qualified okes and I dont want to ask a mate to look at and repair/adjust/modify. I want to DO IT MYSELF.
Now, just bought this old girl: (Dont know how to insert my pics on this forum yet)
The day i got her, she was going fine. Not 100% if I opened her up, but I was assuming that she needs some TLC, some fine carb adjustment, new spark plugs etc.
The next day, I took her out on the open roads with my friend. We rode the whole day, but at approx 5pm in the afternoon, she started to cut out, almost seemed to me as if she was running out of fuel. This could not have been possible, I thought, as I filled up the tank just before heading out the rather deolate, winding stretches of road along side the ocean.
So, I thought the petcock was blocked up. Eventually found a little pud with a guy that had some tools. Stripped off the petcock to clean the inside tank filter, but alas, the filter was clean.
Went on like this for quite a while. Eventually I got to a gas station and filled her up again. Immediately saw that the fuel just runs straight out again from overflow pipe on Carburetor No.2. I jumped on and rode her home, knowing now that I was actually running out of fuel the whole day en that float levels/stuck float bowel would probably be the problem.
Next day I took the carbs off. Adjusted and cleaned a bit with my limited knowledge, interweb and haynes manual.

Seemed to have fixed the problem of the petrol flowing out of the no.2 Carb. Took it for two short test drives and everything was fine again.
the next morning, I wanted to ride her all the way to work. It was raining, so I thought it would be a good test for the old girl, as I believe that water and older bikes tend to not go very well together. About 2km from my house, in the rain, she died. I pushed her all the way to a biker pub in the area and left her there untill I could return after work to check her out.
She stood in the drizzling rain that whole day. I took a bike mechanic with me and he could also not get her to start. Eventually I asked a random home owner if I could just get her his garage, just to be able to work a bit dryer. Eventually, after drying, cleaning, reconnecting, sealing, spraying, trying to start, she started and I could just just get her home, while running very rough.
The day after, I started to investigate a bit further, learning about the coils etc. I clenaed the areas where the points are, put new gasket and sealer. She started easily by this time, but was still missing quite badly. Then only, I replaced the spark plugs and she was perfect again. Again, rode her the whole day last Saturday and towards the end of my trip, once again she started to idle/rev rough and now she is standing again, parked. Starts immediatly, but misses like crazy. The spark plugs are black and smell like petrol. I cleaned them with sand paper, put them back and she seems to be missing even more than before I cleaned them.
I understand that this is a mounth full and I understand that there might bemany different probelms, but if you guys are kind enough to share some of your experience in this dept., I will take your advice and tick off things to be done to the old bird one by one, untill she can purrr across many miles of open roads.
