And please there was no India. Just a bunch of sprouting Hindu Kingdoms and Muslim Nawab's vying to remain alive from being eaten by larger kingdoms. There were differences among Marathas, their alliance with Rajputana & Punjab had tuned bitter and there never was a single battle, East India Company fought on their own. Getting alliance and bribing generals was easy.
Wrong. Mughal Empire was considered the legitimate "Empire of India" and the Mughal Emperor symbolic Emperor of India from north to south. Both Marathas (until their end in 1818) and EIC (until the middle of the reign of Emperor Akbar II) issued orders, coins and documents in the name of the Mughal Empire. That "Emperor of India" title was snatched away by the Britons in 1857 after they brutally massacred the imperial family and burned Delhi until it was dust.
Marathas were considering taking the title of Empire of India from the Mughals back when they were the sole huge empire in 1760, but then catastrophe at Panipat happened and their plans never came to fruition. In the end Mughals retained the title.
The concept of Bharatvarsha or 'India' has existed since at least 1200 BC and both Mughals and Marathas considered themselves a part of the unified Indian identity. This is what prompted the Marathas to start their rebellion and expand their empire in 1730s the first place - they wanted Hindus rulers to replace Muslim rulers within the territory of India. Eventually their goal became the unification of all India through whatever means
They usually bribed generals not through money but through threats - postimperial Maratha states were too small to resist.
After battle if they ensured a very luxurious privy purse to some prince/peshwa who have already lost, then it was not because their heart had grown as large as that of Alexander the Great but they had reason to do it. To secure their dominance.
Your lack of knowledge is appalling.
Firstly, Alexander did not have a large heart and simply retreated out of kindness - his troops simply refused to cross the Indus and tributaries after having seen the turmoil in the thick of the fighting against Porus, who was just a small king with a small army. The real treat was the far larger Nanda Empire who was already alert and aware of Alexander's invasion, and had planted almost all of their giant, well equipped army (at least 300,000-400,000 strong by estimates, with at least 4-5,000 war elephants) on the other side of the river and along the western Ganges for the very same reason. Alexander's men didn't want to fight more bloody and tedious battles like that of the Indus River against Porus, certainly not a series of them against a far larger, stronger and more prepared enemy, among other factors. This caused them to disobey his orders to march...and eventually Alexander angrily gave in and started the journey back westwards.
Similarly, EIC had no big heart. They openly massacred nobles' families like Nazis or IJA would in their respective genocide campaigns. The privy purses were not luxurious gifts, they were barely adequate funds needed by the former Maratha Emperor to maintain his remaining palace now that his empire was gone. In a lot of cases, the Britons simply snatched the palaces that couldn't be maintained and destroyed them (like in Jhansi).
What else propaganda have you been smoking?