It is possible that none of your ancestors were immigrant but colonial. I consider my ancestors who came here before the country was founded as colonials. Those that came after were immigrant. If you consider the colonials immigrants then you have to consider the Native Americans as immigrants as they came from East Asia. Actually in that sense people are descended from immigrants everywhere.
This is the type of information that probably is fairly easy for those who are descendants of immigrants from late 19th century and onward. However, if a good part of your ancestry is colonial, they could have come from places all over Europe(not necessarily what had been termed the British Isles) and your family has lost memory of them. There are teachers who don't understand this. Perhaps because they came from a background of descendants from those immigrants. In many areas of the Northeast particuarly, they lived in their own neighborhoods, married among their own and naturally they know quite a bit about the origin of their ancestors. I know a man who grew up in the Northeast(he is in his late 70s). He said when he was growing up the saying was, "stick with your own kind."
If your ancestors have been in Texas since around 1900, they no doubt started in Virginia or the Carolinas and migrated in different generations, maybe through Georgia and Alabama before coming to Texas. Back then they were too busy to keep records where grandma and grandpa came from. Vital records weren't kept by many states and counties until the first part of the 20th century. It was all in the old family bible. Still a mother after her first child was born immediately made records of that baby, by the time she got to her 9th, she had so much to do, that child might be almost grown before she found time to put the information in the family bible. Now if they wound up in the central part of Texas they might have been German. In San Antonio, they might descendants of the Spanish colonials that settled there in 1731 when Texas was still under Spanish rule. Also some might have been Native American.
My maternal grandmother was 100% Southern American colonial. What I have found is that she not only had ancestors at the first permanent English settlement in the Americas, Jamestown, Virginia(that was before the pilgrims came over on the Mayflower). She had ancestors from Northern Ireland. She had some that were Alsatian German and French Huguenot and some that came from around Pomerania, all before there was a United States of America.
It take awhile to come up with all of that information.
Taylor is an English names but that doesn't mean all your ancestors on your father's side came from England, no way. One thing the root person of your surname was a taylor.
Ancestry.Com states Summar is an English variant of Summer.
This is what they have about Summer
English and German: from Middle English sum(m)er, Middle High German sumer ‘summer’, hence a nickname for someone of a warm or sunny disposition, or for someone associated with the season of summer in some other way.
English: assimilated variant of Sumner.
English: assimilated variant of Sumpter.
Irish (Leinster and Munster): Anglicization (part translation) of Gaelic Ó Samhraidh ‘descendant of Samhradh’, a byname meaning ‘summer’. The Gaelic name is also Anglicized as O’Sawrie, O’Sawra.
German: from Middle High German summer ‘woven basket’ and, by extension, a measure of grain; also ‘drum’, hence a metonymic occupational name or nickname from any of these senses.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4
This is what they have about White
English, Scottish, and Irish: from Middle English whit ‘white’, hence a nickname for someone with white hair or an unnaturally pale complexion. In some cases it represents a Middle English personal name, from an Old English byname, Hwit(a), of this origin. As a Scottish and Irish surname it has been widely used as a translation of the many Gaelic names based on bán ‘white’ (see Bain 1) or fionn ‘fair’ (see Finn 1). There has also been some confusion with Wight.
Translated form of cognate and equivalent names in other languages, such as German Weiss, French Blanc, Polish Bialas (see Bialas), etc.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4
This is what they have about Cavender
English altered form of Irish Kavanagh.
Dictionary of American Family Names
This is about Kavanagh
Kavanagh Name Meaning and History
in Wexford, an Anglicization of Gaelic Mac Caomhánach ‘son of Caomhán’ (see Kevin). MacLysaght says that this is a famous branch of the MacMurroughs. The name is said to have been acquired from the first Kavanagh having been fostered by a follower of St. Caomhán.
Anglicization of Gaelic Mac an Mhanaigh ‘son of the monk’, from manach ‘monk’, a rare Mayo surname.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4
This is about Hutson
English (mainly Lincolnshire): patronymic from the medieval personal name Hudde (see Hutt 1).
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4
They have nothing about Weschey
You need to put this on your teacher's desk and if you are a parent of a child, give it to his/her teacher. We find teachers give outrageous assignment to kids for this type of thing and sometimes they are guilty of intrusion when they ask kids to do their family history.
Names in themselves do not tell the origin of someone's ancestry.
Edit: If your ancestry goes back to colonial times you won't be able to find where they originated by census records, because the census records before 1850 only list heads of households and do not show the place of birth. It might take you 10 years just to find the place of origin of one ancestor.