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What else can I do to help him increase his odds?
There is not much YOU can do to increase his odds, other than help him research his best options. It is up to the discretion of the consulate officers to accept his application or not. My advice is to be truthful but do not volunteer information if they do not ask for it. Only give them the information they ask for. Also, he may need a translator if he does not speak fluent Serbian, in which case you must arrange that with the consulate beforehand and submit the translator's passport and details to the consulate.
Not all US consulates will accept non-residents for interviews. It is up to the consulate and its at their discretion. Some consulates will not process Russian applications regardless of residency status, so you will need to contact the consulate beforehand. Either call them or email them for answers. Each one has different rules and regulations.
According to their website, translators are not allowed in the waiting room. So it may be possible they do not allow translators at all, you will need to verify this directly with the consulate.
Note: All nonimmigrant visa applicants are expected to speak either English or Serbian at their visa interview. No interpreters will be permitted in the waiting room. Please note that this designation for Russian applicants does not guarantee that a visa appointment will be available for all applicants in the above designated visa categories.
If Serbia does not allow tourist visa interviews for Non-Serbians, you will have to find somewhere else nearby, such as Budapest that will allow it.
Do visa paid services increase the odds of success?
In my opinion and experience, no they do not. They simply fill out the paperwork for you and ask you to provide all the evidence and personal records necessary to apply. So you essentially do the work for them anyways, they just fill out the paperwork, which isn't too hard. They also schedule your interview appointment for you, using the same website you would have to use. So you do not gain much.
If you decide you want to go that route, I would suggest finding a Serbian visa service that works with the US Consulate there already. Those types of companies will have translators and package deals ready for you.
Unfortunately there is not much you can do to guarantee he will get a visa. They look at many factors and do thorough background checks. It is difficult to accept Russian tourists as many of them are fleeing their country permanently, so there is a risk he is not a genuine tourist. The officer will need to figure out and determine this, and the best thing your boyfriend can do is be honest, be calm as possible and be friendly. A good joke to break the ice always goes a long way in my experience. They will want to know why he is visiting the USA and he can let them know he has a girlfriend there. They will also want to know if he intends to overstay or will return home. If he has a job in Serbia, he can show proof of his job offer, and show he has ties and a reason to come home. He could even get his employer to write a letter but generally USCIS doesn't accept such magic letters in an interview. He can bring whatever paperwork he wants but in our experience, they rarely look at that, and focus more on background questions and to see if your story adds up or conflicts.
It is entirely possible that they suspect he is fleeing or dodging the draft in Russia and they could deny him. But if he has a fair interview, he should have nothing to worry about.
Also, the current wait time for a B category visa (tourist visa) in Belgrade Serbia is 6 days. So that is very good news! My in-laws had to wait 12 months for an interview in Budapest!