Is it necessary to have reservations for train and bus travel for getting around Northern Wales in August?
It's not necessary to book in advance for local travel, no. Make sure you check in advance that there are bus and rail routes where and when you want to travel though, as public transport in more remote areas can be uncommon.
The best way to see Northern Wales is to drive your own car. We have driven in North Wales on 2 trips with no problem. The bus system operates from hubs...so you can waste lots of time going miles and hours past where you want to go....so you can take a dog leg back. Because of the jagged coastline you have a lot of dead ends where you have to go out and back. The Mountains invite you to get out and see the countryside...you can only do this with your own car. Go with someone who can drive and you won't be sorry. If it seems that renting a car is too expensive...remember that your time is worth money too.
You cannot have a reservation, you must purchase a ticket :-) and there is no need to do so in advance.
http://www.arrivabus.co.uk/ runs all the bus network you are likely to need and you probably will be able to find value in 'a day rover' (or whatever the current title is) if making several journeys per day.