Yes absolutely, regarding marriages.

While I cannot speak to the exact nature of marriage/hostage relationships between the Romano-British, Celtic people, and immigrant newcomers as there are very few textual sources to draw on, there was certainly intermarriage between the various groups of people milling about in post-Roman Britain. Indeed the emergent Anglo-Saxon and Welsh cultures are far more accurately described as a melding of the new groups rather than a creation of ethnically homogeneous populations. This is evidenced by a wide variety of new creations in material culture that draw from both Insular and Continental antecedents, examples include new housing patterns (both styles of houses and where they were located, there's evidence of mixed "neighborhoods" that included both continental and insular styles of housing) in eastern England, jewelry styles in elite burials that blended Scandinavian patterns with Roman ones, and burial patterns that incorporated both "pagan" and Christian elements.

These societies that started to spring up across modern England and Wales were far more heterodox than is normally assumed. In addition to the native Roman-British and the well known newcomers from Saxony and Jutland, there were also Irish, Pictish, Scandinavian, and other continental populations that moved into modern England at the same time. The resultant Anglo-Saxon and Welsh societies were instead created through a process of assimilation and dominance by a new found elite that traced their legitimacy to different period in history, but they were not as ethnically distinct as is popularly imagined.

Later sources indicate customs of wardage (famously the probably apocryphal Haakon the Good of Norway was raised in England) were indeed present in England, but it is unattested at the time of the migrations in the specific area, (the use of hostages, marriages, etc... is relatively well attested on the continent) though to be frank many practices are unattested at the time due to the extreme scarcity of sources from the time. So while it is possible that hostages and wards were used to create peace and agreements between these societies, it is impossible to say for sure given our current evidence.

To build on u/Steelcan909's great answer, we can now use genetic evidence from ancient burials to answer some of these questions.

Several grave sites across England have been selected for genetic tests in recent years. These are from Linton, Oakington and Hinxton (Cambridgeshire), York and Melton (Yorkshire), and Norton Bishopsmill (Durham), and date from the Iron Age, Roman and Anglo-Saxon period. It is in fact possible to genetically differentiate native Britons and incoming Anglo-Saxons, and in this regard the early Anglo-Saxon cemetery from Oakington is particularly interesting. Testing was carried out on four skeletons, all of whom were later determined to be women. Two of these women were found to be Anglo-Saxons. One was a Briton. However, the last showed signs of mixed ancestry.

This shows that in this community, at least, there was intermarriage. The evidence goes against the "mass invasion" model, in which the Anglo-Saxons push all the Britons into Wales and Cornwall. But it also goes against the "warrior elite" model, in which a small number of Anglo-Saxon men rule over a large population of Britons. In fact, judging by the grave goods found at the Oakington site, the two Anglo-Saxon women were poorer than the British one!

Due in part to new evidence such as this, historians/archaeologists/linguists are increasingly arguing that the notion of a single Adventus Saxonum is a myth. The migration seems to have continued over a long period (possibly more than two centuries), and probably took different forms in different places. In some areas, particularly in East Anglia, Essex, Kent, and the south coast, whole communities from across the North Sea could have simply moved over and plunked themselves down on British turf. In other areas, new settlements were created with both Anglo-Saxons and Britons living together. Some British communities might have simply continued on, and shifted to using Old English at a late date.