Love Affair with Germany

1)actually, if you cycle on the street, you cycle on the right.
2.) you can google using "fahrradverleih" - I found this:
http://www.antrieb.com/vermietung.php?gclid=CPfQs-T1xZICFQtBMAodtRZqYQ
3.)I am not that much into cycling, but 180 km sounds way too much. In three days you would be in the Czech Republic. 180 km is more than 100 US miles, if that helps you. If you drive 6 hours, that means an average of 30km/hour. That is very fast for being on vacation.
4.)in springtime there can be ocassionally some more water in the river, and maybe some streets will not be passable because of the flooding. maybe you have a wrong impression what "flood" means - there is not a Tsunami taking place, there is just some water dipping over the rivers edge, and I really would not worry about this.
5.) I really do not know why someone should do something like this - please take a train or hire a car.

In my biking days I found 15km/hour a pleasant speed, which I could do for quite some time. That would mean about 90 kilometer in a day, if you bike for 6 hours. Realise that the country is not flat and that every now and then you have to go uphill and this can diminish the amount of kilometers per day.

Cycling ,like driving, is on the right, passing on the left. If there are cycle paths, they have to be used, no cycling on the street in this case.
180 km per day in six hours - 30 km per hour - is not my idea of a leisurely pace.

1) On the right. This applies in Germany for all traffic, even trains go on the right (if there are 2 tracks or more). And - albeit not required by law - you can notice this also at places where many people walk in 2 directions.

2)
List with addresses where you can rent a bicycle. Please note that service like www.nextbike.de or www.callabike.de are only for getting around in the city.
Normally you cannot return the bicycle at another place. Since DB stopped there luggage car services years ago, I've not seen this offered. You can however transport the bicycle on regional trains by yourself. Back to Dresden. Or also useful if you did not get as far you liked or if the weather is really too unfriendly for cycling.

3) 30 kph an average is too high. There are situation where you have to slow down (other cyclists or pedestrians) or where you have to stop (crossings). To achieve an average speed of 30 kph you would need to have a travel speed of 40+ kph. That's not easy, not even on this rather flat terrain. Calculate with 20 kph. Keep also in mind that there are a number of interesting places along this route (Meissen, Torgau, Wittenberg, Dessau).

4) Floods are not that common. And if they are either before May (spring floods) or after May (summer floods). They also don't come by surprise in this part of the Elbe. If you would plan a cruise the unstable water levels of the Elbe could be a problem. Albeit low water is more common than high water. Floods which would affect also the cycle paths are rare.
map with water levels

Germany Tourism has lot's of information on cycling in Germany.

Bahn&Bike a useful (thick) brochure by DB about bicycles on trains. You can take your bicycle on regional trains. (Day) Ticket for this is EUR 4,50. There are however some regions and states where this is for free. E.g. in the state Saxony-Anhalt (Magdeburg).

We spent a few days cycling in the "Sächsische Schweiz" region last year. However, we only did day trips and mostly into the mountains/off-road. We based ourselves in Stadt Wehlen which is close to many of the beautiful sandstone formations and right on the Elbe (half an hour from Dresden by train). Our hotel had bicycles for free - but they were of such poor quality (only 3 gears - not possible to get up hills) that we arranged for mountain bikes to be delivered to us the next day. We hired our mountain bikes from "Peers Bike Adventures" who are based in Dohna but deliver and pick up bikes again for a small fee. I agree that 180 km per day is too much!

Maybe it's better to buy a Second Hand Bike. It's possible to get one up to 40,- Euro, but you have to organize in advance. To rent a bike could be more expensive than to have bikes on your own.

You might want to consider the route from Prague or Usti Nad Labem to Dresden. It would be amazingly beautiful and you'd be able to pass through Sächsiche Schweiz National Park, with its picturesque sandstone formations and idyllic villages. There are countless rental sites online where you can rent bikes. You will absolutely love this corner of Germany. I lived in Dresden for a bit as a student right after the fall of the wall, and continue to consider it my "second home". Have a great time.
-TB