futni is Infinitive? as in the T&N your example verbs are shown as tanul and siet, not like tanulni and sietni ) must be so?
"futni" is infinitve. Hungarian dictionaries don't give you the infinitive, they give you the third person singular because that's the shortest version. You just add "+ni" if you wan the infinitive.
Even in Hungarian courses, the verbs are always given in the 3rd-person singular. I don't know any other languages that do it like this, but for Hungarian, verbs are always communicated in this form, rather than in the infinitive. Yes, infinitives end in "-ni", and most can be formed by adding "-ni" to the 3rd person singular form. (There are several irregular infinitive formations, though. I think around 10 or so.)
I think Hebrew is similar, in that it has an infinitive but the dictionary form is third person singular perfective/past.
Ancient Greek had an infinitive, too, but the dictionary form is first person singular present indicative. For Latin, that seems to be popular as well in dictionaries but some glossaries I've seen use the infinitive, some the first person singular present indicative.
And some languages have no infinitive so they have to use a finite form, such as Modern Greek (which uses first person singular present indicative) or Maltese (I've seen both third person singular perfective/past, as with its Semitic cousin Hebrew, and second person singular imperfective/present, meaning nearly all verbs were sorted under t-).
Arabic is the same as Hebrew. If i'm not mistaken the third person singular past is used
I believe that they use 3s past, too, but I think that unlike Hebrew, Arabic has no infinitive form that they could use.
It's a little complicated, but I try explain it. You can use both of them for a person and also for an object. For example: "I love you" - "Szeretlek", "I like you" - "Kedvellek"/"Tetszel nekem". "I like that movie" - "Tetszik az a film"/"Szeretem azt a filmet", "I love that movie" - "Imádom azt a filmet".
It is not incorrect to say that you "love" an activity in English: we use it all the time, so "I love running" or "fishing" or "playing poker" is correct; also the infinitive works just as well, as in "to run" etc.
Could you please explain, why we sometimes put the verb at the and of the sentence, and sometimes at the beginning?
It is complıcated. The word order is quite flexible, the stuff that you want to emphasize can go to the front. There is a standard order, kind of like a neutral statement, and any deviation from it changes the emphasis.
Szeretek futni. - I like running
Futni szeretek. - It is running (and not something else) that I like to do.
I suggest you read up in the comments of previous lessons, there is quite an extensive discussion on the subject.