In another question, I read that to begin with a budget of 250 Euro max, I could get a bridge camera. But are there any with the possibly to change the lens?
Having a non-interchangeable lens in an SLResque body with a compact-camera image sensor is pretty much the definition of a bridge camera, so I think you are out of luck :)
You might want to look into the four-thirds system instead or one of the other mirrorless jobs, but 250 Euro isn't enough to get into it I think.
It depends on how you define the term. Generally, no.
"Bridge cameras" are a category that "bridges the gap" between point and shoot cameras and something better — where "something better" is usually understood to be a DSLR, and the idea that it's a "bridge" usually implies that it has advanced features and manual control — but it also might mean that it's a relatively bulky superzoom, which might not really offer a lot of control or even high image quality but kinda looks like an SLR, and so "bridges" the difference only in appearance.
Some might even argue that this size/weight similarity is the most important part of the definition, and that relatively advanced compact cameras like the Fujifilm X10 or Canon G12 don't count, because even though they have high image quality and advanced manual control, they're not the right size and shape. Or, someone might put the line somewhere between those two models, arguing that the X10 is too compact to count.
To add to the confusion, in the time since the term was invented there's a new category of cameras: compact mirrorless interchangeable-lens system cameras. The lower end models of these are designed to compete with P&S cameras, and the higher end models to compete with digital SLRs, so in that sense these are very much "bridge" cameras — but since "bridge camera" had a meaning long before this category existed, they typically don't count.
From the point of view of your particular question, the starting price for these interchangeable cameras is generally much above your maximum of €250 — so from that practical standpoint, you are probably out of luck. You may be able to find an older-model or used Olympus Pen or Sony Nex for not too much more — but you should be able find similar-vintage DSLR in the same price range, so if the reason you're looking at this type of camera is simply cost, that doesn't simply the decision.
Assuming that "bridge" is in the old sense (and @mattdm gives a nice explanation here for why it may not), then you still have the option of getting a "bridge" that can accommodate a lens add-on. For example, the Canon S5IS (old, but this is the one I have for reference) has compatible wide angle and tele converters that can be attached to its lens to effectively widen the zoom range of the camera. Surely more modern compacts have similar options.