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Likely the best spot to get onto any of the highways is the Q1 gas station on the B202 in Osterrönfeld. With a little bit of patience, one should at least be able to get towards South, with a little luck also towards North, as the B202 continues towards the highway interchange between the A7 and A210. Only drawback: I'm not sure how to get here on foot. However, take a look at the section towards East below, which explains one possible spot to hitchhike to this station.
North towards Flensburg, Schleswig, Eckernförde,
In order to get north, for example onto the A7, you should try your luck on the B203 in Büdelsdorf. The roundabout at the end of the city is in theory a good spot, but cars cannot really stop there. If you go a bit further, you should be able to find little roads to fields, which are better suited. There are also two gas stations before you exit the city (Classic and Jet), where you can also ask the drivers directly, however most of the traffic is likely not leaving.
East towards Kiel,
To go to Kiel, you can probably find a spot on Berliner Str. The intersection right next to the Esso gas station has a lot of traffic and is close to the B202, but also still deep inside the city. You can probably ask for a ride there, but most of the traffic will be local. There are bus stops closer to the B202, but I can't tell if they are good.
Another option is to check the spots in Osterrönfeld, you just need to cross the canal by tunnel or ferry.
Blackriding on the buses is almost impossible unless the driver's cabin is empty or closed off (due to Covid). Usually, the drivers take a break at the central station and you can get in unseen, but there is still a possibility that they will ask for your ticket when they come back. There are however no dedicated ticket inspectors.
Accommodation and Sleep
It should be possible to find decent places to camp near the Eider river and the canal. Try checking Google Maps for spots with a sufficient amount of trees and stay away from houses. It is likely more suitable to camp on the Büdelsdorf side of the river as well as the other side of the canal (crossable by tunnel or ferry). In both cases there is a good possibility to meet people walking their dogs in the morning. Ironically, you're likely to be left alone at parking spots for commuters.
Other useful info
There are several places downtown offering free wifi, such as the Rondo, Sparkasse, McDonalds, Backwerk or the city library.