Are the English (Anglo Saxons) distant cousins of the Dutch

Genetically speaking, if the population of Scotland and Wales taken out of the equation, the Dutch tend to form the closest genetic cluster to the English, closely followed by the Irish. See for example, this paper in Nature. Though this various regionally, with various studies suggesting that the overlap with the Dutch is greater in East and South of Britain, which of course mirrors the generally accepted migration pattern of the Anglo-Saxons.

It's important however to note that the English are not the same people as what are commonly referred to as the Anglo-Saxons. That is to say, yes the Anglo-Saxons seem to have contributed a significant amount of genetic make up of the English population (between 10 to 40%, it varies regionally) but so did previous waves of migrants to reach Britain, such as the people generally referred to as the Celts and before that neolithic farmers.

Secondly, the people that historians call the "Anglo-Saxons" did not form a single or exclusive group in their own time. Various small groups, perhaps even family-sized units of Germanic-speaking migrants came to Britain during the Migration Period and the idea that an entire organised tribe transplanted itself in a kind of organised migration has long since been abandoned.

given that they seem to have originated from the same region in the northwest of Germany that is around where Netherlands is

Ultimately, most historians assume that all Germanic tribes, or at least their ancestors, expanded southwards from what is now Northern Germany/Southern Denmark. Though this initial expansion predates the emergence of the Anglo-Saxons by several centuries.

It is often said that the Anglo-Saxons came from what is now Northern Germany, but technically, this is somewhat incorrect. The Anglo-Saxons, or rather, the majority of the people which later linguistically dominated what we call Anglo-Saxon culture, came from the Jutland peninsula (modern Denmark) and the coastal area running up until the Heligoland Bight, an area which is significantly more compact and smaller than "Northern Germany".

The Dutch, or rather, what was to become their language, did not originate in this same area, but rather adjacent to it; between the Weser and Rhine river. In modern times, this area only partially corresponds to the area in which Dutch is spoken, due to migrations period events; which saw the Franks move more towards the west, with Frisians and Saxons moving in from the Northeast. The descendant languages of these latter groups (Frisian, followed by Low Saxon) are actually more closely related to modern English than Dutch is. Though Dutch is indeed the closest major language to English.

and the fact that old medieval English texts seems to resemble modern Dutch?

They do, sometimes to the point that (especially in their earliest form) they can be hard to distinguish from one another.

I wouldn't go as far as to say that Old English resembles modern Dutch though. Yes, there are many instances in which an Old English word will resemble a Dutch word; sometimes the modern Dutch word appears to more closely follow Old English than modern English does; for example in the case of cyning and koning (king) or weorold and wereld (world).

Overall though, modern Dutch and Old English aren't that similar, with Old English being far more grammatically complex and isn't readily readable for modern Dutch speakers.

This is a pattern mirrored by all extant Germanic languages today with regard to their Early Medieval forms: German is often regarded as a grammatically intricate , but modern German is baby-talk compared to Old High German and even Icelandic (which is a very conservative language) is somewhat less complex than Old Norse.