Yes you can do short term internet but there are a couple of snags.
Firstly - you will have to pay for installation (€50) and a minimum of 3 months rental.
Secondly - you can disconnect for free. However, every time you want to re-connect there is a charge of €30 and you jhave to pay for a minimim of another month.
Reception from a penthouse in phase 2 should be fine although there are some very adverse comments going around at the moment on various other forums about Teleast. One comment I found said that they were paying for a 6Mb link in Los Alcazares bit were only getting about 2Mb most evenings.
Teleast used to have 2 websites - 1 of which is just a holding page, the other is no longer active.
However I found the one for Internet Mar Menor who are effectively the same company
http://tvhoradadamarmenor.com/