Did you check the tire pressure?

No, I have no tool to check it, but I was there with the mechanic the whole time and he didn't pump air or anything like that. I rode about 300 meters to the shop after I got off the bus, and it felt different as soon as I left the shop. The dérailleur also leans to the right side now - why is that? It's on first gear... I think its too tight, which is also why changing gears is much harder now, but I'm still a newbie in this so I'll wait for more input.

To Test the Tire Pressure, squeezing the tire With your hand, Thumb and Forefinger, and feeling the resistance to your effort is Remarkably Tool Free..

The right looking at it from where? The Back of the bike? the side?

Many riders check the tire pressure with a gauge before every ride. A gauge is probably a good investment. They are not very expensive. After a while you can tell what's good enough, just by squeezing the tire.

Do you live in a location that gets very cold in winter? This can effect the battery, tires, and grease.

Lift the rear wheel and give it a spin to make sure it's not rubbing the brakes or frame.

I guess it's too late to ask now, but when you immediately turned around and took the bike back to the shop, what did they say?

It feels like before, but that's not an accurate measurement.

From the side. I don't need a gauge, I can just drive to the nearest gas station which is less than half a mile away and pump the tyres to my favorite pressure. It's relatively cold here, but Israel never gets as cold as some US states (its 46 degrees F right now, which is what we consider rather cold),

It seems fine. I also remember the mechanic spending some time on that.

I didn't take it back to the shop after they fixed the gears. I was just hoping that, by the time I rode home (8km), the stiffness would be gone.