I am unfamiliar with the types of maintenance your automatic transmission might benefit from at this stage of its life that cannot be performed with the transmission in place. In general, I would not go replace things that are not showing any sign of needing attention. Like seals.
The timing chain tensioner is at the front of the engine and is not affected in any way by the ring gear wear issue. The timing chain tensioner is "activated" by the engine oil pressure, and maintains a preload on the timing chain (which turns the valve camshaft(s), depending on model you may have two overhead camshafts, which operate the valves) to keep it tight between the sprocket at the crankshaft and the sprocket(s) on the camshafts. Tension on the chain keeps it from skipping a tooth on one or more of the sprockets. A bicycle chain on a 10 or more speed bike has a thing on the back sprocket, called a derailleur, that does the same thing.
In the car the chain tensioner has a hydraulic unit that should be able to be replaced directly by unbolting it and installing a new unit with a new seal. The hydraulic assembly has a cylinder and piston arrangement that has a rod attached on the end of the piston. The rod engages a crescent shaped rail inside the block, below the camshaft sprockets in the front of the engine. The rail is fixed at one end (usually at the bottom of the engine block) by a hinge pin. As the oil pressure increases the rod extends, pushing against the rail to make it pivot inward to apply pressure against the outside surface of the chain. The rail is fitted with a low friction layer of material to avoid metal to metal contact with the chain, which prevents wear and keeps things quieter than they otherwise might be. If the chain tensioner hydraulic unit internal seals are worn, then it should be replaced. I do not think replacing the hydraulic unit will help much if the rail material is worn off, as in that case you need a new rail. The range of the stroke in the new hydraulic unit will be the same as the range in the old one, so if the chain is not held tight because the rail is worn too much, the new hydraulic part will not address the problem.
The chain tensioner will have no direct affect on lifter noise. The lifters are part of the valve actuation scheme, but are contained on the head, in the space above the valve and below the cam on the camshaft. It is normal for hydraulic lifters, which in a Mercedes and other vehicles act to automatically adjust valve lash or free-play using engine oil pressure so there is no longer a need to mechanically adjust valves, to be less than full of pressurized oil at start up. As oil pressure builds, they should fill up, then expand to the desired dimension to take up the excess clearance, and quiet down. If you are experiencing a lot of valve clatter at startup, it is possible you have an oil pressure problem (low oil pressure), or it is also possible the chain clatter/slap from a loose chain is being mistaken for lifter noise.
As for the starter, the teeth on the pinion gear should be visually examined when the ring gear is replaced. If the teeth are damaged the starter should be swapped for a rebuilt unit, or you can have yours rebuilt. I would not think the cost of having a new gear installed and tested would be much different than a rebuild job.
Good Luck, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)