It goes with the verb in this case. "Hålla i" means something like "hold on to"., whereas just saying "jag håller dig" sounds kind of... rude. Like holding someone's arm to not let them go, or something like that.
Noteworthily, though, is the fixed expression "hålla handen" ("hold hands"), which does not have the "i" but remains nice and romantic nonetheless.
I don't understand. You said that Jag håller dig is like holding on to someone's hand to not let them go. Isn't that the kind of holding you would be doing if someone were falling off a cliff? Am I missing someone? Or is it more like Jag håller en kopp. Where it's more about having something physically in your hand that you can carry around with you?
¿Estás seguro? Dudo muchissimo que tengas que decirlo así. La preposición "a" se necesita para establecer la referencia a persona como objeto directo. La policía es una entidad, no es una persona (en contrario a "el policía".) No estoy seguro, pero Goole me halla una million de googleitos buscando "llamar la policia" (incluyendo las comillas), mientras que "llamar a la policia" solamenta alcanza 412000 resultados. Puede que ambas sean correctas, no obstante...
Sorry for my bad spanish, but my english is even worse and probabely not good enough for those abstract things...
You've come to the right language, Swedish has a lot of them. :)
ögon is the plural 'eyes', the singular is ett öga. The odd plural is because there historically used to be a special "dual" form to say "two something", and only that form survived for that word (also ett öra, två öron 'an ear, two ears') but only the real plural survived for most other words.
English native speakers and even dictionaries seem to disagree among themselves. See this discussion for instance: https://forum.wordreference.com/threads/hold-onto-vs-hold-on-to-bitterness-a-hand.550309/