Learn Portuguese (Portugal): O principiante anda a tentar não cair no gelo. - The beginner has been trying not to fall on the ice.

While está a tentar simply means "is trying" right at this moment, using the verb andar as an auxiliary in the structure andar a + infinitive describes an action that has been happening continuously or repeatedly over a recent period. This is why it translates perfectly to the English present perfect continuous: "has been trying".

Could I place não earlier in the sentence, before anda?

You could, but it would completely change the meaning. The negative word não must go directly before the specific verb it negates. If you wrote não anda a tentar cair, it would mean the beginner "has not been trying to fall". By placing it right before cair, the sentence correctly conveys that they are actively trying not to fall (não cair).

Why do we use the preposition no (the contraction of em + o) for "on the ice"?

English makes a strict distinction between being "in" an enclosure and "on" a surface. Portuguese groups both of these spatial concepts together under the single preposition em. Combined with the masculine definite article o, it becomes no gelo, which is the natural way to express being "on the ice".