electrical problem

invest in a multi meter. When you say alternator seems to charge slowly is that a guess? or you know for a fact. With old cars you need to becarefull with bad connections and rust. check and CLEAN all connections. For the battery. with a tester or multimeter measure alternator. Usually alternators crap outwhen its hot so drive it around for a while and test it again. If readings are low alternator is bad. 2nd check the battery. When battery are discharged it cant be charge to 100% anymore. The more the battery is discharge the more the battery cant hold charge. So make sure the battery isnt worn out/old. 3rd check resistance in wires. you sohuld not have more than 5ohms of resistance in any of the wires. If you still havent found out whats up your screwed haha. Then you will have to find whats staying on in the car and causing the battery to crap out. For the bulb issue check to see if the left and right side bulb is the watts. The reason it blinks faster is there is less or more resistance in the circuit. Check the blinker relays someone might have changes it with a wrong one or a diff one to make it look kool or something. if that dont work your going to have to check every wire to find the high resistance or if things are wired wrong.

you probably have a short in a wire somewere in the car, the short discharge the battry a make a trouble in your right turn signal