Okay, well first of all, I would probably consider the idea that depending on a players level it would increase the potency of a spell, this allows a player access to a large range of spells, while still promoting advancing their levels and abilities.

Forcing a player to "spend time" is debatable, remember the purpose of a game is to extract a person from reality, but at the same time there needs to be some reward for work, it's an idea worth tinkering with anyway in my opinion.

Regarding advancement, you could combine the two ideas: Allow the 'level' of the mage to apply some base enhancement to each spell cast, such as increased base damage dealt/shielded. Alongside this, you could allow the mage to learn a basic form of each spell and, with repeated use, allow them to use a more advanced form.

I like the idea of 'drawing' power from the environment. Reminds me of the ability to draw from enemies in FFVIII. How about drawing 'reagents' from the environment and giving (some, if not all) spells a specific cost that is needed to be able to cast them? You could also include the research element here, study the collected reagents to learn more about their effects?

Should there be some sort of spell research system where a mage spends time in their library or laboratory to become proficient in the spell?

This is a really cool idea. The concept of research is something I think could work really well in a practical setting.

As to how one can achieve this, I would tend to think that to call it spell 'research' while nesting outside of tedium will be a challenge. Personally I would consider research to be something that you could use to help intertwine the character-power mechanics with the elements of the world. For example, a fairly basic idea that might be interesting food for thought could be a means of using the loot from certain enemies as a means to 'transmute' (to some degree) reagants that would be forever with the player from that point. I think this could be a really good way to promote exploration and side questing.

Rough example: you get the "fire heart" of some demon breed/elemental or something that is found in some area that is non obligatory, however obtaining the heart and transmuting it with some means will allow you to permanently have the potency of the heart stored in a stone you created which is simply regarded as some sort of extra passive ability, i.e an ability that buffs your fire, or allows your area of affect fire spells to affect a greater range.

As for doing this within a laboratory, that could lead to some epic feelings of progression and adventure as you venture out and back into your lab to create a trinket that would empower you. This coincides nicely, in my opinion, with your approach to have your mage "draw" energies from other places, rather than simply conjuring it. Not only this, but the breadth you could push this mechanic to would be immense, spanning throughout the entire game as a means for people to get tangible benefits from exploration.

Keep in mind this is just an idea. There are many, many other ways. Maybe this is just something to serve as food for thought.

The background to the system is that the mage could 'draw' energy from the surrounding environment, and channel that to cast the spell.

So what exactly are you thinking of? I can interpret this sentence in a couple ways: The player could simply have an automatically regenerating mana pool. Or they could have a 'draw energy' ability that keeps them from attacking/using weaker spells (or possibly even moving) in order to charge enough to use a more potent spell. (The player would just charge their energy to max every time before going into combat, so you might want to limit its use, maybe keeping them from holding on to energy for too long.)

Perhaps different types of spell would use different types of energy and so the player would have to pick which spells they want to be able to use (they might have a cap on total energy). Perhaps different areas would have different energy concentrations, adding a tactical depth through maneuvering. Or certain areas could be drained of energy, either just because they have a limited amount, or by using a specialized 'drain energy' spell (that would of course be less efficient than 'draw energy', if it exists, but could deprive an enemy mage of power).

That kind of switched from interpretation to brainstorming half-way through, didn't it.

Perhaps different areas would have different energy concentrations, adding a tactical depth through maneuvering.

Now that's a cool idea. That would be such a good way to ensure the game has good pacing too as well. The only problem would be creating a system that's too complex early on, but I suppose that could be counteracted by the environments at the start being fairly basic. That would be really good to work in adventure while justifying it with different means of magical power / experimentation. That's the sort of thing that if any part is removed, the core is broken.

by using a specialized 'drain energy' spell

I don't really understand this, do you mean something that could allow a player to intentionally drain an area of magical power OR a player? Or would it only be used to drain the energy of an environment which an enemy seems to be specializing in?

Another idea might be that they have to learn fire from say, studying a flame and learning the properties of it. That way it forces the player to travel to obtain new skills, and you can keep the higher level stuff in areas that are harder to reach.

What would studying entail? I feel like that is the key to making the process more interesting than simply "go to place x and pick up flame y and get skill z."