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You are right; a good emergency fund will help you hold your bitcoin for the long term because it will be enough to take care of your unforeseen problems, and you will not think about selling your bitcoin to solve those problems. Since you are still in college, I will advise you to reduce the money you will be using to accumulate Bitcoin weekly to 10% and increase your emergency money to 10% so that it will be enough to care for your unforeseen problems and allow you to hold your bitcoin for the long term.
Emergency fund is not an ongoing expense. Once you establish it (such as having 3 months of expenses.. or maybe you want to have more than 3 months?), then it is established.
Of course there is the concept of float and reserves too, and maybe it does not matter so much what these are called, but there still should be practices in place in which you would not spend from any of your emergency funds until you were to exhaust your reserves first... and so there could be a certain urgency to replenish emergency funds that are spent as compared to potentially less urgency in regards to reserves and float - even though all of the extra money that you have likely allows you to be more aggressive in your investing into bitcoin when you have otherwise good financial management so that you would never have to touch your BTC, except completely at a time of your own choosing... which may well be years down the road, or at least years after spending a lot of time building it up and/or otherwise managing and maintaining it.
In regards to some kind of a target of saving and/or investing 20% of your income.. that seems attainable, even though it does sound a bit more than what many folks shoot for, yet any exact percentage amount would be a product of discretion and/or fair assessments of how much discretionary/disposable income the guy has... so then if half of the 20% were to go into bitcoin (that would be 10%) and the other half were to be just kept in cash, then that other 10% could be considered as float or as reserves depending to the extent to which you might designated towards something that you are saving up for, such as saving up to buy a bicycle or saving up to have money for buying BTC on dips or some other purpose that you might keep some extra cash on the sides (even saving up to go on vacation or to take your wife/girlfriend on a date).
On the other hand, if your emergency fund is not yet built up to a sufficient size, such as being 3 months of expenses or more, then yeah there is no problem putting that 10% into the emergency fund until it gets up to the amount that it needs to be and then there would not necessarily be any need to add further to such emergency fund or to withdraw from it, absent some rationale to touch it.