How did people and goods move between East Pakistan and West Pakistan?

Yes, it was possible. There were two entry exit points on West Pakistan India border, one is still active Wagha in Punjab and probably Munabao in Rajasthan. However, because of well connected Rail and Bus service Wagha border check point was/is most preferred. It is learned that there was no problem in civilian movement (though always under Indian scrutiny), but movement of armed forces personnel was almost difficult except for medical reasons or marriage functions etc. Pakistani leadership hardly tried for ease in civil movement or unrestricted travel between the two countries because of their self declared superiority complex that they are better than their Indian counterparts in every term so it was never on their agenda. Again, as Pakistan was getting a lot of aid from Western bloc led by USA, it gave them a false sense of a wealthy state. Needless to mention most of the West Pakistani's hatred towards East Bengalis because of their dark complexion, different language and culture; they found no reason to travel to East Bengal. And, those in Armed or Civil services had a privilege to travel by air at government's cost. The Punjabi and Sindhi elites of Pakistan had (almost) no regret of loss of East Bengal as according to them it was an inferior culture, prone to natural calamities e.g. frequent cyclones and floods, and a place full of poor people who eat fish, speak Bengali, and sympathize with Hindu India.

When we try to assess the future possibilities, both countries should sit together( though onus is more on Pakistan as it seek a false pride in being a Islamic country leaving behind common history of both the countries that today's Pakistan was also a Hindu India before arrival of Islam on this land). Successive Indian governments have always tried to have good and cordial relations with Pakistan; neutral historians can easily figure it out. The future is unification of India, Pakistan and Bangladesh and if thats not possible then kind of a European Union with least restrictions on movement and trade. If Europe after hundreds years of war can be unified then why not India and Pakistan ( and Bangladesh too).

Except during periods of war or high tension, overland travel via India between the 2 wings was possible. However, after the introduction of a visa and passport requirement in 1952, this became much more expensive and time consuming for most people. Prior to 1955, Pakistanis found travel through India more expensive than it should have been because Pakistan hadn't yet devalued their currency while the Indians insisted on exchanging it at par. Furthermore, the break up of the Indian Railways and the new priorities of both countries meant that the Rail connection was neglected. Thus overland travel was possible but costly and difficult.

For commodities, the government enabled the shipping route between West and East Pakistan to be monopolized by a few Karachi based West Pakistanis who charged high prices. Economically, there was a huge drain on the East Wing because Bengali jute had to pay for development of the West wing.

The air link, via PIA (Pakistan International Airlines), after 1956, mainly used by bureaucrats and army officers, was very expensive and often detoured via Colombo rather than flying over Indian territory. This was because the Army realized that they would need PIA in the event of hostilities to air lift soldiers (as in fact happened during the 2 Indo-Pak wars) and thus for strategic reasons a longer route needed to be kept operational. The Indians, whose economy was more dirigiste, worried about smuggling and had little interest or incentive in facilitating overland transport between the 2 wings. However, overland travel was certainly possible except during wartime or periods of increased tension.