Just so you do not land up chasing your tail so to speak. Pull the battery and have it charged and load tested. Both can be had for free at some parts outlets. It's possibly in horrible condition. A really bad battery could have damaged your alternator to some extent as it tried (the alternator) to charge a constantly low and defective battery at maximum output for a long long time perhaps. But to just put a new alternator on might not really solve anything without the battery checking good. You may just need a new voltage regulator on that alternator anyways. Alternator belt is tight? As for the waterpump change you might save enough doing it yourself to pay for the parts to repair your electrical system. To repair/replace the items you have mentioned is not difficult and the sooner one works on their older cars increases the chance of having money in your pocket as well as increasing your comfort zone. If we are to drive older cars save the money for other work. It should not take much effort to find a place to bury it.