Please check my lager procedure

Im about to brew my first lager with my soon-to-be completed fermentation chamber. Please tell me where I go wrong :
1.) Cool wort to 60F and pitch starter
2.) Immediately put primary into fermentation chamber and chill to 50F
- do I need to wait for fermentation to start before chilling ?
- Can I drop temp straight to 50F or must it be done gradually ?

3.) After +-3 weeks (once fermentation is complete) gradually raise temp to 60F for four days.
4.) Rack to secondary
5.) Gradually cool to 35F for four weeks.
6.) Add carbonation sugar and bottle.
- Do I need to add more yeast before bottling ?
- Is it better to lager in the bottle in this case ?
- When fermenting and lagering how constant does the temp have to be ? Is a 5F variation OK ?

Did I go wrong anywhere ?

I always pitch my lagers at fermentation temperatures. Actually, I pitch all of my beers at fermentation temperatures, or even a bit below. So, I when I make a lager, I chill the wort to 50 degrees, and take the starter out of the fridge (where it's been for a day or two, finished) and bring that up to about 48 degrees and pitch the slightly cooler starter into the wort. That seems to work great.

As far as raising the temperature after primary for the diacetyl rest, it's best to do that when fermentation is about 75% finished, so the yeast are still very active. So, if your target FG is 1.016, say, and it started at 1.060, I'd do the diacetyl rest at 1.020-1.022 or so. That will encourage the yeast to clean up the diacetyl as well as finish up the fermentation. Sometimes I miss that, though, and just do it as soon as fermentation is nearly finished.

After the diacetyl rest (and the beer is at FG), I rack to secondary. Then, I gradually reduce the temperature until I'm at a lagering temperature.

I pitch fresh yeast when I bottle. I've done it both ways, with and without the additional yeast, and had good results. But, it's taken a long time for some of the lagers to carb up without adding the fresh yeast! I like to boil the priming solution, cool it, and then add 1/4 package of dry yeast to it. Stir well, and then rack the beer into it. It works great, and I haven't noticed any additional sediment.

For lagering time, I've been going with the rule of thumb of one week per every 10 OG points. So, for an OG of 1.070, I lager for 7 weeks. Sometimes a bit more.

EDIT: Yooper beat me to it as I was typing this, so some of this will repeat what she says.

A few suggestions:

If you can, cool the wort further before pitching. Ideally, you want both the wort and starter at or below 50°F before pitching. As long as your starter was adequately sized, fermentation will take off just fine.

Raising the temp. to 60°F towards the end of fermentation is a diacetyl rest. If you start your fermentation cold as above, you may not need a D-rest. However, some people (including me) do them anyway. Don't wait until fermentation is done before raising the temp. Raise the temp. when fermentation starts to wind down. The technical point at which to raise the temp. (according to the late Greg Noonan) is 6 points short of expected final gravity. If you do it when the krausen is falling, you should be fine.

Depending on your OG, you may be ready to rack in 2 weeks. My lager OGs are usually around 1.050, give or take, and I'm always ready to rack in two weeks, including D-rest.

Your lagering time of four weeks is probably OK, but more accurately, take the last two digits of your OG and divide by 8. This is how many weeks to lager. (That's an average lagering time calculation and there is more to it than that, but it's a good standard.)

As long as you don't lager for more than 6 weeks, I wouldn't worry about adding yeast at bottling.

Bulk lagering is thought to be better for the beer than bottle-lagering.

Small fluctuations in temperature during fermenting and lagering are OK, but I would make efforts to keep it minimal.

Both replied make sense - thanks.
Do you ferment the starter at room temp or at pitching temp ?