Doing daily or complex activities without attachment Is it truly possible to do activities without expectations or some aspect of the self ideal attached to them? Does the Buddha explain anything of the sort?

If yes, how to go about achieving that? It could be something like what the Bhagavad Gita says.

We could do those tasks mindfully, but they could be complex thinking activities, necessary to achieve some final goal, so we cannot dismiss them as "thinking, thinking". Consequentially, there is a chance that we may get lost in our thoughts and feelings may creep in. 

Maybe this is another question, but did the more complicated concepts and practice techniques Gautama described attach to the context of that day and age? And maybe they are only best suited for monks? (Maybe we shouldn't take them to the workplace or family.)
In Buddhism things are slightly different. Being aware and mindful of what you do (as you say) is more of a hindu concept if it is from the Bhagavad Gita.

This itself is good. A surgeon, ballerina, acrobat, etc. will need to be mindful and aware. If they do not then they cannot do their job. This will make you do a good job in whatever you do.

In Buddhism what need to be done is you should be aware of the arising and passing away of sensation you experience with equanimity. (Pahāna Sutta, Avijja Pahana Sutta 2) This is what will eradicate the 3 evil roots which in turn helps you realise nirvana.