1) "будем ездить" assumes multiple actions, so it is not suitable for one trip, you may say We will go there every summer (multiple actions) - Мы будем ездить туда каждое лето. 2)comparatives like меньше/больше/лучше/хуже чем [smaller/bigger/better/worse than] require the nominative case, if you don't use the "чем", comparatives require the genitive case 3) "вижу" means see something with your eyes "вижусь" means meet people and spend time with them

1. Ездить has a repetitive meaning. There and back again. Again and again. Будем ездить means the same for the furure. Поедем - we will go... (or we are going... I think it has to do with something planned). Поедем (or maybe a little better to say едем if it is planned?) implies there and back again if you do not add anything else. 3.) Вижусь с друзьями. Видеться is a reflexive verb (reciprocal). It means "see each other/one another". It takes at least two to do it, here we have you and your old friends, you see them and they see you. Why "с"? Because it is a mutual action. (There are other verbs used with с, lots if: гулять с, жить с, говорить с, смотреть с, видеть с...in all these examples it takes at least two do something, but it is so to say one way street, if you say "видеть с друзьями" you will receive the following meaning: you and your friends see something together, you are going to see a concert, you saw someone rope walking or you and your friends will see Hobbiton next year.) Видеться с, встречаться с, целоваться с is like two-way street, what you do you recevie in return. Целоваться с: you kiss someone and you are kissed in return, someone who you kiss kisses you back. Драться с: fight with each other, you hit someone and someone hits you back. Встречаться с: you are dating with someone, you come to spend time with someone who comes to spend time with you.

I feel myself such a spammer, especially after Natalia's answer... 3.2) Я никогда не вижусь с моими старыми друзьями. Why "с" needs to be in this sentence? In this discussion: https://www.italki.com/notebook/2838820/entry/816229 one of your questions was: "Книга написана им. Is this genitive or instrumental case in Russian? Why isn't "по" in this sentence? Such as Книга написана по им? We would say "the book is written by him" in English. There is no "by" in Russian." And one of the answers was: "So there is 'by' in Russian and it is... Instrumental case." Although it often works, it is not always true. For instance: 1. "By" in "by the way" is definitely not expressed by an instrumental case. 2. В детстве я хотел стать космонавтом. = In [my] childhood I wanted to become a cosmonaut. Here the word "космонавт" ("a cosmonaut") is in the instrumental case ([Стать] КЕМ? — КосмонавтОМ), but the English translation does not contain any "by" preposition. That rule works, when we say "smth is done BY SOMEBODY" and in similar situations: Книга написана ИМ. = The book had been written BY HIM. So, the sentence: Я никогда не вижусь С моими старыми друзьями. does not mean: I never meet WITH BY my old friends. but rather it means: I never meet WITH my old friends. Anyways, when we say "with [somebody]", it is "с [КЕМ-то] (instrumental case)", not "с [КТО-то] (nominative case]". For instance: Сегодня мы встретились с друзьями (not "с друзья"). = We met with our friends today Мы пошли с ними (not "с они") в кино. = We went to the cinema with them. Please, note: when we use prepositions and when we do not, some pronouns may also differ, despite they are in the same (instrumental here) case. For instance: Книга написана (no preposition) ИМ. = The book had been written BY HIM. Она пошла С НИМ в кино. = She went to the cinema WITH HIM. Both "им" and "ним" are translated as "him". Both variants are "он" ("he") in the instrumental case.

2) Туалет меньше ванной комнаты. In English "a < b" is always pronounced like "a is less THAN b". If we omit "THAN" ("a LESS b"), it would be unclear, which one is more small: a or b. But in Russian, there are at least two variants for the sentence you've provided: A) Туалет меньше, ЧЕМ ванная комната. Since we used "чем" ("than"), it is clear, what is bigger and what is smaller, so both "туалет" and "ванная комната" are in the nominative case, which is used in the dictionaries. B) Туалет меньше ВАННОЙ КОМНАТЫ Since no separate hint words are used, we change the case of "ванная комната" and make it genetive to remain clear. Why is it the genetive case specifically, not any other one? Honestly, I cannot answer this question now. Maybe, because we compare the properties of two objects (sizes, more specifically), we use the genetive case for expressions like "размер ваннОЙ комнатЫ" ("the size OF the bathroom", and this is the situation for the genetive case). Maybe, it comes from construction like "'a' is big/small. But THE SIZE OF 'b' is even bigger/smaller [than the size of 'a'"). Anyways, since no word "THAN" is used, one of the objects should be in the different case.

1) We are going to Mexico next year. Should I use Поедем or Будем ездить assuming it is just a trip? Does a verb's Perfective Aspect usually mean two ways or one way? There are at least 3 variants to express different situations: A) Мы поедем в Мехико в следующем году. = We will go to the Mexico city next year. B) Мы съездим в Мехико в следующем году. = We will take a trip to the Mexico city next year. The difference from A) is that we describe the whole trip, including coming back, while A) describes only our intention to go to Mexico city without any specific notes on coming back. C) Мы будем ездить по Мехико в следующем году. = We will be travelling around the Mexico city next year. Here I used this verb in the imperfective aspect, which is analogous to English indefinite (simple) or continuous (progressive) tenses (depending on a situation). But it is used, when we want to focus listener's attention on the PROCESS of doing somthing, not on the result/intention/decision. The general thing about prefixes is they not only can change an aspect of the verb (turn the tense into perfect, for instance), but also can act like prepositions in English, or change the situation (for instance, "ПОйти" = "to go [somewhere]", "ПРИйти" = "to COME"). They are not just aspect modifiers, and sometimes a different prefix can change the sense drastically. An example of similar behaviour in English is "to look FOR" and "to look FORWARD", the only difference is the separate words are used in this example. But we generally tend to use prefices, suffices, etc for that, so, one Russian word can be often decomposed into two or more English words. For instance, "подарок" means "a present", and "подарочек" is "a little present" (we can also say "маленький подарок", but it is a more rare case). I've almost exceeded the 2000 characters limit for a message, so, I will split my post into several ones.