How to travel in Europe as a gap year for cheap?

A. Italy, Germany, Switzerland and Poland are perfectly safe. Safer than America for sure. Russia is dangerous though. If you go to Russia, it's complicated with the visas and accommodation and I highly suggest you don't go to any bars don't stay ina a cheap motel / hostel, and stay alert at night. If you're white and you don't draw undue attention and you stay in the wealthier areas, you'll likely be fine, but it is certainly a dangerous place. Also, if you're not white - don't go. Just don't.

B. Amersterdam is also safer than America. Murder can happen anywhere and is more likely to happen in America. Best to stay away from hard chemical drugs, but weed never hurt anyone.

C. Backpackers that travel Europe or elsewhere on the cheap use hostels, not motels. Check them out online. Personally, I don't like sharing rooms with smelly hippies, so I used to pay a bit more for a single room at hostels. Very cheap. Also, check here about getting a Eurorail pass for travelling to the different countries. They give discounts to students: https://www.eurail.com/en/eurail-passes/global-pass.

D. Just my opinion here, but Switzerland is boring. There's nothing of interest. You'll see all the same architecture in France and Germany. I'd pass on Switzerland and opt for somewhere a little different. Czech is very fun. Ireland would give you a different feel. You're right on with Poland, it's great. Spend your time in Krakow. There's a bar in the dungeon of the 500 year old castle downtown called "Carpe Diem". Check that out. Fun times.

E. If you want to make some money as you travel, you can easily work for a week and move on by picking grapes in France. Backpackers commonly do this. Quick cash. Meet people.

F. One last thing - don't bring the bedroom and the kitchen sink with you. Just one medium sized backpack. If it doesn't fit in there, don't bring it. I see too many kids trying to haul around an apartment on their back and one on the front. It'll be miserable to carry all that around all the time.

If you're a US citizen, working won't be an option - there are no work visas or options for gap year jobs in Europe

So if you want to travel, you'll need to save up enough first.

Macedonia is cheap and safe

No, you're completely uninformed. Safety is not the issue here at all.

You can't legally work in any of those countries, for a start. You'd require a visa for each country, and they are not easily acquired.

You might be able to volunteer for a time, which would involve living somewhere for a few weeks and essentially working for bed and board, and sometimes pocket money, but you won't make a great living at it, and you would have to check out the bureaucracy side of things too. Google Wooffer and find out more about this.

And FYI, tell your mother that anyplace in Europe is way safer than anyplace in the US, and that friend of hers probably overdid the drugs and had a bad reaction, attacked someone and then had to learn the hard way that drugs don't work for everyone. Only 2 years? He was lucky, he could have completely disappeared.

Countries in Western Europe are expensive. Eastern Europe is much cheaper and so is Southern Europe (Spain, Portugal, Italy, Greece.) Stay away from crook-states like Russia, Serbia, Georgia (basically every former USSR country except the Czech Republic and perhaps Poland) if you are concerned about safety. Wherever you go, don't do drugs, not even in Amsterdam, it is silly and it doesn't bring you anything.
Preparation is key. Read up on websites before you go, plan your stay, plan your finances, plan your travels. I would not advise hitchhiking, but public transport is brilliant in most of Europe. Effective, cheap, as fast or faster than driving. Flying within Europe is also dead cheap if you use price-fighter airlines. I can recommend Skyscanner.com to find tickets. It is not neccesarily faster than taking a train, however.

I lived in Germany for 9 years. You need to look into staying at Youth Hostels. Research them now before you leave. And make sure to print out their info so you'll have it handy. Getting around is easy to learn. Check into getting a Eurail Pass. You can get on and off trains in any city. Staying safe is just like here. Be observant of your surroundings and the people you party with. Basically, if you feel unsafe then you probably are. Pay attention to your gut instincts. I've traveled and vacationed in over 24 countries (many times) on 3 continents and NEVER ONCE felt unsafe. And I'm talking about walking around in large cities all night long. Saving money? That's a relative thing. Depends on your diet. The small kiosks are relatively cheap especially gyros and kabobs. What I liked was McDonald's and the other fast food places sell beer, but not to go. You can tell the young people traveling by their large backpacks. Leave your suit cases at home and travel as light as possible. Train stations have baggage holds where you can leave you big packs in a locker and walk around with a smaller day pack. Water...is not free at restaurants. If you ask for it you'll have to pay for it. Try learning some of the languages for the countries you visit. Yes, no, please, thank you, you're welcome, excuse me, and where's the bathroom always come in handy. I used to know at lest that much in 14 languages when I was younger. Enjoy yourself.