Buddha's relation to Hinduism Q:


  Did the Buddha copy Hinduism and add his own stuff? Why is Buddhism
  connected to thoughts in Hinduism if he didn't do so?
'Hinduism' did not exist when the Buddha was alive, as follows from Wikipedia:


  This "Hindu synthesis" started to develop between 500 BCE and 300
  CE, after the end of the Vedic period (1500 to 500 BCE), and
  flourished in the medieval period, with the decline of Buddhism in
  India
  
  Wkipedia: Hinduism


When Buddha was alive, the religion of the Brahmin priests we call 'Brahmanism', which was far more limited in scope than Hinduism, per the stock description from the Pali suttas below:


  Now at that time the brahmin...had mastered the Three Vedas, together
  with their vocabularies, ritual, phonology and etymology and the
  testament as fifth. He knew philology and grammar, and was well versed
  in cosmology and the marks of a great man.
  
  MN 91


The Three Vedas are explained in Wikipedia as follows:


  The canonical division of the Vedas is fourfold (turīya) viz.,
  
  
  Rigveda (RV)
  Yajurveda (YV, with the main division TS vs. VS) 
  Samaveda (SV)
  Atharvaveda (AV)
  
  
  Of these, the first three were the principal original division, also
  called "trayī vidyā"; that is, "the triple science" of reciting hymns
  (Rigveda), performing sacrifices (Yajurveda) and chanting songs
  (Samaveda). The Rigveda is the oldest work, which Witzel
  states are probably from the period of 1900 to 1100 BCE. Witzel, also
  notes that it is the Vedic period itself, where incipient lists divide
  the Vedic texts into three (trayī) or four branches: Rig, Yajur, Sama
  and Atharva
  
  Wiki


If you read the Brāhmaṇa Vagga in the Majjhima Nikaya, there was no Hinduism. In fact, Hinduism, as inferred by Wikipedia (in the 1st quote above), probably copied from Buddhism. 

For example (while I am happy to be corrected), I do not recall reading in the Pali suttas any detailed discussion/debate between the Brahmins &amp; the Buddha about respective theories/doctrines of karma &amp; reincarnation. In the little I researched, I found no systematic doctrine of karma &amp; reincarnation in the Three Vedas. Even when I browsed some later 'Upanishads', I found no mature systematic doctrine about karma &amp; reincarnation (apart from the ideas of one certain individual philosopher). 

Again, if we read the Brāhmaṇa Vagga in the Majjhima Nikaya, we find the Brahmins were similar to the Hebrews (and probably many other tribal groups), where their belief system was about how they were 'God's chosen people' or 'born from Brahma's mouth/breath' (while the other castes were born from lesser parts of Brahma's body).

Some useful links from Sutta Central, with lots of links, books &amp; research, are:


The early Upanishads: a nice introduction to the pre-Buddhist tradition
Rebirth &amp; reincarnation in the Brahman Vedas


Note: While the Pali suttas never mention the 'Upanishads', the reincarnation orientated leader of Sutta Central, namely, Bhikkhu Sujato, appears intent to follow conventional historians rather than follow the Pali suttas, in his efforts to back-date the Upanishads to prior to Buddhism. If we place our trust in the Pali suttas, we find what existed prior to the Buddha was the Three Vedas &amp; their accompaniments. 

An answer about this topic by Bhikkhu Yuttadhammo is here: Did the Buddha ever mention the Upanishads or the Vedas?

Lastly, if you wish to be a real Buddhist, it is not possible to believe the Buddha copied any of his core teachings from Brahmanism/Hinduism because the suttas say what the Buddha taught he "never heard before". "A Buddha" cannot copy other doctrines otherwise he/she cannot be called "A Perfectly Self-Enlightened Buddha" ("Sammasambuddha"). 


  'Arising, arising!' — At this thought, monks, there arose in me,
  concerning things unheard of before, vision, knowledge, understanding,
  light.
  
  'Cessation, cessation!' — At this thought, monks, there arose in me,
  concerning things unheard of before, vision, knowledge, understanding,
  light."
  
  SN 12.10
  
  
  
  Vision arose, insight arose, discernment arose, knowledge arose, illumination arose within me with regard to things never heard before:
  
  Dhammacakkappavattana Sutta