I think a key thing as spy is to avoid groups completely. If you reduce the chances to bump into someone then it will make life easier.
I think spies work best when they are trying to pick off the people at the back of the lines, whether it's people running from spawn, or engineers or people going back for health. Kill, cloak, hide.
If you're in a situation where, when cloaked, you're trying to get through a group of enemies, either following, or running through the front line to get behind the enemy, then I highly recommend jumping from side to side. Being able to reduce the area of possible contact with an enemy is the key.
When disguised there is a little bit of timing involved, as well as a clear plan. You need to look like you have a definite movement, nothing gives away a spy as someone just running around after another person. If you attack when they are attacking then it's easier to blend in and not look suspicious.
I do my attacks as spy in a forward motion. Cloak, get in behind the lines, disguise, decloak, run forward with the enemy attackers and attack. No matter the result, I push through to my team-mates, heal and resupply. Rinse and repeat. Obviously if your using the cloak and dagger or dead-ringer then it's different.
There is a huge slice of luck involved with tracking and pushing through as a spy as people are a little unpredictable and sometimes you just get unlucky.
As a spy, you're best off spending your time working to assassinate the opposing medic. Since the other team has only one medic, it is a huge advantage to your team if you can kill (or badly hurt) the other medic, even at the expense of your own life.
Since this is a competition-level play, you can expect full communication from the other team. You will very rarely fool them into thinking you're on their team. They all should know where everybody is. (Whether or not they really do is another matter). The simplest way for you to be effective is to find a nice sport to Cloak and Dagger, wait for the enemy medic to run by, and revolver or ambassador them from a distance.
Mix up your spots, be unpredictable, and stay hidden. You may also want to spend some time hounding the enemy sniper, depending on his skill level. I've seen highlander teams completely fall apart from a skilled enemy sniper. On the off chance he's razorbacking, the ambassador will be the weapon you want to go with. Mix your disguises, but definitely use the sniper disguise - that class matches closest with this play-style.
Best Answer
Yes.
You can still switch to one of your weapons and press B to switch your disguise weapon to the corresponding weapon slot. For example, holding out your sapper and pressing that key equips the disguise's secondary weapon.
Your disguise health also matches whatever health the enemy you're disguised as has at the moment you wear it (but your real health remains the same). If the disguise is low on health, you can try to trick an enemy Medic into healing you, so that both your fake and real health will go up.