is travelling to havana cuba without a package deal doable?

Answer 1

I've been to Havana several times, on a package deal and otherwise. Most people prefer to stay in private accommodation, as it is a way to meet the people and feel part of the scene. (On one such trip the local boys were calling round to invite our boys to play football each day! How much more welcome can a person feel?) Here is a website which will enable you to make such arrangements:
http://www.acrosscuba.com/

Answer 2

yes but you will need to find a hotel that has vacancies when you get there.the package deal seems easier.