1. Your instructor is 'performance' flying. Sounds like you're 'attitude' flying, which is better. Others above have already described why you're doing the right thing.
2. I'm with your instructor - anticipate and turn the heading bug first. It gives you an excellent visual reference for the turn and let's be honest, takes about 3 seconds at most to do. If it's an outbound to inbound turn, set the bug say 10 seconds before you are due to turn and turn it in the direction you intend to turn.
Another reason I'm big on this is it's preparing you for appropriate autopilot and flight director usage in the future. You might not have these yet, but you will in your career in the not too distant future. If the AP is engaged you will have to turn the bug first. If you're flying just using the flight director, and you don't set the heading bug, you'll be flying opposite to the FD bar indications. The last 3 CAR217 organisations I've worked for have been big on not turning contrary to FD bar indications etc.
3. I'm with das uber soldat, who actually provided the reference too - your instructor is correct with this one. That's unless I'm misunderstanding your discription of events. Are you talking about the timing for the sector entry or timing for the hold - they are two different things and I think a few ppruners have this confused too.
Last thing you need to think about - pprune is full of many opinions, and many are uninformed and based on a lack of knowledge. Don't ever take pprune knowledge as gospel (some might even think I'm full of ****e). Sit down with an instructor or two and get them to explain why they want you to do certain things. Just because someone shows you a different way doesn't mean it's wrong. It's up to you to decide what tips/tools you take on board to better your flying.