¡Hola! I have started learning Spanish recently using resources teaching Mexican Spanish and I’m also going to start Spanish lessons with a teacher from Mexico. I am wondering since there are so many varieties of Spanish,
1.Are all of them mutually intelligible?
2.What is/are the difference(s) between Spain, Mexican, South American Spanish?
3.If I were to speak Mexican Spanish in Spain, would I be understood?
It would be good if I can get some insights here 
¡Muchas gracias! 
There are obviously many differences (I’ll leave the experts/native speakers to weigh in on those!) but yes to 1 and 3, based on my own experience.
I learnt European Spanish and when I was in the USA, I went to a weekly Spanish meet-up for both native and non-native speakers which included a couple of Mexicans and many other hispanohablantes from all over Central and South America. They didn’t have any problems understanding me, I didn’t have any problems understanding them (apart from problems linked to me only being at intermediate level, I mean!) and they seemed to understand each other at least as well as Brits and Americans would understand each other in English, with only the accents and some vocabulary being different.
The only systematic differences between European and American Spanish that I was aware of beforehand were that the 2nd person plural vosotros(as) form is only used in Spain and ce-, ci- and z- are only lisped in Spain, though not even in all parts of Spain. I managed to avoid using vosotros but lisping ce-, ci- and z- in Spanish is second nature to me now, so I didn’t always manage to stop myself doing that, but nobody seemed to notice anything out of the ordinary, so I doubt you’d have any problems if you spoke Mexican Spanish in Spain.
Anyway, good luck!
Prosody is the thing that changes the most.
I’ve found that « y/ll » is the pronunciation that will vary the most. It will either be pronounced « y », « dj » or in Rioplatense Spanish a soft « j » (like in French or Portuguese) or « sh ». It depends on the regionn and the person.
It shouldn’t stop speakers with various accents to understand each other, especially if they know that the other is a foreigner, they’ll be more careful 
Of course all of them are mutually intelligible, but there are a few differences between each other, and as a Mexican I just came to say:VIVA MÉXICO !!! saludos desde Oaxaca, México y si alguien desea hacer Tandem inglés-Español o alemán-Español just let me know bis bald
¡Hola a todos! I wanna ask Spanish learners how do you memorise/remember spanish conjugations? Do you memorise conjugation tables or just by remembering examples?
I am having a hard time on conjugations because it is so different from the conjugations that we have in Korean 
It would be great if I can get some suggestions from Spanish learners @RonP @mmlemonade @StevenT
Muchas gracias 
Hola Jinyoung! Todo bien?
When I started to socialize in Spanish and to have hispanophone friends, I struggled with this a lot too! I knew the words but I couldn’t talk fluently because I would stop everytime a verb came in my sentences.
What I did is that I used the quizzes conjuguemos.com like craaazy, until I got 100% in every quiz. Now, things are much better
¡Hasta pronto!
I am by no means fluent in Spanish but I know a bit about the dialects. In general people from different regions will understand you. The only exception is Argentinian Spanish. People can understand each other but the dialect is very different. Again I am not fluent and could be wrong but this is what I have heard and learned from personal experience. Buena Suerte!
Indeed all of the dialects are mutualy inteligible, the basic vocabulary and the standard versions remain quite similar.
My only recommendation is paying attention to idioms, different meanings of the same word, humor and the order in which ideas are organised in a sentence.
Even inside Mexico I find many troubles in explaining or saying certain things with others due most of Mexicans (as most of Spanish speakers) tend to omit certain information or asume their ideas are clearly enough stated. In my defense, I take my time to explain others why things are not so ovious.
Romance language speakers value and defend their views on cordiality and etiquette. Thus they appreciate explanations much more than direct or detailed messages (my personal style, unfortunately).
So, misunderstandings between people of diferent regions and economic groups are quite common and adding the wrong words in the wrong order might be interpreted as offences, arrogance and pity (clearly said or implied in other ideas).
But, you shall not fear. The best you shall do for avoiding those confusions and misunderstandings is consulting any of the all the abundant webpages which explain local specific slang or simply asking for explanations to the local people, most of Spanish speakers prefer giving funny explanations of their slang rather than turning around and leaving you alone to figure out things by yourself.
Some example of vocabulary with terribly different meanings, which you shall be cautious with are:
Peninsular and Colombian highlander vs Mexican = cojer (to handle, to take something, to use something or to choose for something Ex. cojer camino para A= to take a certain route to A , BUT not to use in Mx)
Peninsular & Mexican vs Caribean = bollo (a bread or a ball of non cooked bread, too explicit in Cuba)
Colombian vs Mexican & Peninsular = carajo (any unuseful thing or annoyance in Co, but used for inciting confrontation for certain people in Mx and a larger number of people in Sp)
Mexican northern vs southern = piloncillo (too private for describing it for people in the north, innocent home made sugar in the south).
Mexican vs Peruvian = maleta (a simple lugage in Mx, a prostitute in Pu).
Peninsular vs southern Mexican = hostia (a common religious item in Mx, to beat someone in Spain)
Peninsular vs Mexican = pepe (not going to explain its meaning in Andalucia but it is a common nickname in Mx).