Average speeds for crits would be somewhere in the 24 to 26 mph range in Cat5. Of course, that's only the average and includes the slow bits as well as the parts closer to 28mph. Road races - it depends on the terrain.
Tips for going up hill:
Find a pedalling cadence that's best for you. Sounds obvious but many people think we should all 'spin like Lance' which is all well and good but we don't have to race for 8 days in the mountains at the end of a 3 week Tour. Rule of thumb - whatever gets you up the hill the fastest for your current state of fitness is what you should use. If you need to work on increasing cadence a bit in climbs do that during training and not in racing.
Press really really hard on the pedals and if the gradient changes slightly change gear accordingly. It's easy, if the gradient slackens just a tiny bit to confuse your legs hurting from the recent effort and not with the current easier part. If you see the gradient ease up a even just a little, click the gear into the next smaller sprocket. It'll hurt but you'll get over it... or take up knitting.
Tips for going downhill:
Always look at where you need to go. Never look at the big drop off the end of the cliff. Remember - hands follow eyes, bike follows hands.
Look to see if you can see the corner exit as you enter the corner - as with riding in a bunch, don't stare just infront of you. If you can see where the apex and exit of the corner is then life if good.
Relax. There's lots to do on a bike going down hill fast. You need to be loose on the bike and shift weight around accordingly. Don't apply the "deathgrip" to the handlebars but conversely, don't hold on too loose otherwise when you hit a bump you'll likely be pitched of. Falling off at speed hurts, especially if you slide into something solid that refuses to move. If you want to get all aero and hold on to the center of the bars near the stem, hook your thumb under the bars. Having your hands slip off the bars followed by a faceplant to the stem at 40+mph is bad. What follows is often filed in the "I don't want to know what happens next" archive.
Get nearly all of the braking done before the corner and before you lean the bike over. Look up "traction circle". You can brake really hard in a fairly straight line, you can lean the bike over a long way with no brakes on. Brake hard and lean over and your backside will be sliding across something really hard. A visit to the hospital and bike store for new shorts often follows.
Speaking of braking - it's better to brake a little too much going into a corner than it is not enough and having to scrub of a bit of speed by using the brakes in the corner. The former will allow you to achieve the correct racing line and you can easily add speed on a descent by getting back in the tuck and not using the brakes. The latter means that you''ll take some really silly line through the corner and end up exiting the corner way too slow.
Lift the inside pedal and put lots of weight on the outside pedal.
Don't keep the gear in the 11 or 12 sprocket on technical descents - if you have lots of tight corners to sprint out of, use your gears.
If you're doing a road race then try and take a drive around the course before the race or "massage" your route to the start to include parts of the course. Use something like google earth or mapmyride to check out the terrain and see if there's any likely points of interest.