Your dealer sounds like he may be trying to gouge you a little but there are many items on the Monty that are the owners responsibility. Light bulbs are usually owner responsibility. If you bought the rig from this dealer you'd think he'd make even those types of things "good". Especially if he wanted good word of mouth advertisement or for you to buy as a repeat customer. He may be making a big mistake.
If you've ever read any of the posts here on the MOC you'd know that the gauges do NOT work or work only sometimes. Most of us have learned when the tanks are full or nearing full. It is no big deal. If you really want gauges that work you will need to install some that work from the outside of the tanks. They work well but are very expensive. Most manufacturers all install the same type of gauges. Again the dealer seems to be making a mistake by charging you for dealing with this issue. Either he should have told you up front what he was going to do and charge you. You could then have taken care of it yourself.
Unless you have a "sealed" battery ten months is way too long to go with it plugged in and NOT refilled with water. I believe he may be mistaken about the landing gear operating only on the battery. I believe they will work directly from the converter. But the battery is an owner item. Here yet again the dealer is selling himself short by not "serving" you well. He could have simply replaced the battery at his expense in the name of good customer relations. But the battery IS your responsibility. The battery should be checked at least monthly if plugged in to shore power. More often if very hot climate or heavy electrical usage. You may very likely need a new battery.
Check the search function to find out about battery process. There are many discussions.
You do not need any chemical for the tank. It will not clean the tank and even if it did the same thing would happen again very soon. We started off using the chemicals but soon stopped. They do not work. They are expensive. To keep your black tank clean you should always keep the valve shut, even if hooked up to sewer, and use more water. It is not possible to put too much water in the black tank.
When you dump you should dump the black tank first then follow up with the galley and or gray tank. Then use the flush function. I close the black tank valve and let the flush fill the tank about half full or so. I keep doing this until the water runs clear. If you don't have one of the clear elbows then invest in one as soon as you can. They are great! When the water is clear then close the valve and put in a few gallons of water. This will get you started good for the next round. Take the chemical back and save your money.
I'd take the offer of about $100 bucks to get out of the current situation. Next time you will be in a much better position since you will have so much more info at your finger tips.
Good luck and keep us informed.
HamRad