To “travel” inside a house?

Solution 1:

a) Can “to travel” and “to make a trip” also be used in this way in English?

To travel is not used for movement inside any building with the possible exception of using a vehicle of some sort. (Wheelchair; forklift truck, etc.)

To make the trip can be used to indicate a great distance and/or a tedious journey. It is also possible to use this as a form of emphasis or exaggeration -It is casual/informal.

"That's the tenth time I've had to make the trip up those stairs! If you want anything else, you can get it yourself!" ELU, Greybeard 2021

to make/take a trip - "I have to take a trip to the toilet/bathroom" - can be used informally - it is informal but it does not indicate the distance, which may be quite short:

From "Oscar Murillo: the build-up of content and information" - Page 34

during a long-haul flight I'm interrupted only by a trip to the toilet, or by a neighboring passenger asking to exit the row

and

An Ongoing Investigation - Page 327 by Timothy Daniels · 2014

He poured another and made a quick trip to the bedroom, where he kicked off his shoes and socks and pulled on a pair of slippers.

b) Are they formal or informal in this context?

Informal.

Solution 2:

Trip does not necessarily indicate a long distance. You can have a trip to Tibet for the summer, a trip to the market to buy some chicken, or a trip to the toilet after eating some bad chicken.

Travel in contrast would be unusual in any local context. If I travel for work, it typically means I am going out of the area— flying, or perhaps driving for several hours, in order to reach the work site. I commute to my office in the nearby city every morning, I do not travel to it. The business traveler is a different kind of worker from the commuter.

If you want explicitly to draw attention to the distances within a large or spread-out house, I wouldn't suggest either trip (which does not necessarily imply distance or difficulty) or travel. A hike or trek would be more evocative, or even journey, whether employed as a verb or a noun. A haul might be suitable if carrying something, although this can connote burden or difficulty rather than distance.

She made the trek from the kitchen to the music room twice.

She hiked from the kitchen to the music room twice.

She went from the kitchen to the music room twice, each time a journey.