What if Russia abolishes serfdom early, how could it have affected their history.
I like the question but, unfortunately, the short answer is "this was not going to happen" or, as Catherine II put it, "if I abolished a serfdom, the nobles will kill me before peasants would come to save me".
The timing is all wrong. It could happen either almost immediately after the Time of Troubles or at least prior to the reign of Peter I when the serfdom system was transformed into the de facto slavery (Vasily Golitsin presumably had some plans in that area but it is not clear if he would be permitted to conduct such a reform even if regency of Sophia lasted for a much longer time; the government did not have funds to keep nobility on a payroll or to compensate it financially) or it could happen after the Napoleonic wars (at least after 1812 there was certain sentiment fed by the patriotic BS about the "peoples' war", etc. and after 1814 some of the European experience kicked in as well). But it simply could not happen in the mid-XVIII because all the necessary conditions had been lacking.
When emancipation happened (admittedly, it could happen few decades earlier):
(a) Russian Empire had state bank and long history of the paper currency so that idea and practice of credit and land-based loans was already there for the decades.
(b) A big percentage of the estates had been already used as a collateral for the loans given by the state-owned bank, which gave government a big leverage in conducting reform.
(c) While most of the land had been owned by a nobility, there was already a significant split between "service" and "land owners" nobility. A considerable percentage of the nobles serving in the military or in the civic administration did not own any estates/serfs and relying upon salaries (and, well, bribes, if possible) and pensions rather than upon the income from the estates, which many of them simply did not have. Plus, by mid-XIX a considerable part of the civic administration were not from the noble class at all and to some degree this applied to the military as well: both in a military and civic service person could obtain a personal nobility by reaching a certain rank (but a person could reach an officer rank while not being a noble) and hereditary nobility by reaching a higher rank but obviously these people did not inherit any estates from their parents. While this was less common for the higher ranks, it was still quite possible even on a very high level by the early XIX: in 1812 Barclay de Tolly (Minister of War, full general, commander of the 1st army), while being from a noble family, had no estates or serfs. Such a split meant that functioning of the state mechanism would not be seriously impacted by the reform.
(d) There should be a general recognition of the fact that serfdom is obsolete as economic and social phenomena.
Now, at the time of Peter III:
(a) Peter III only planned creation of the state bank. This was implemented during the reign of Catherine II in 1768 and its main function was issuing and exchange of the paper currency. The 1st paper currency was introduced only in 1769. The 1st truly commercial bank (State Commercial Bank) was created only in 1817. Massive development of the credit and bank system started only in 1860.
(b) The bank providing loans to the estate owners had been created during the reign of Elizabeth I in 1754 (with branches in St-Petersburg and Moscow) with a right to give loans of 500-1000 rubles with land as a collateral. In 1766 that bank started giving loans to the peasants: 20 rubles at 6% annual rate. During the reign of Catherine II capital of that bank reached 2 millions but the rules never were clearly defined and as a result in 1786 the bank was closed. In 1796 a new State Loan Bank was created for supporting the estate owners: it was giving loans (with estates, houses and factories as a collateral) for 20 years at 8% annual. Still, even in the 1820's the practice of mortgaging the estates in that bank was relatively new (see, for example, "
The Squire's Daughter" by A. Pushkin: an noble who mortgaged his estate is considered by his neighbors as a very shrewd thinker).
(c) After reforms of Peter I
all Russian nobility had to serve (with a "compensation" being conversion of serfdom into a de facto slavery). With the state not being able to pay salaries in a timely fashion due to a shortage of cold, silver and even copper, income from the estates, even a small one, was a serious factor and doing something drastic could create serious unhappiness in the military and in the civilian administration as well. Taking into an account that in the Guards even majority of the soldiers and noncoms had been from a nobility (in 1762 Alexey Orlov was a sergeant of Preobrazensky Regiment and Gregory Potemkin sergeant of the Horse Guards), this experiment would be suicidal. Peter III issued a law about "Freedom of the Nobility" which eliminated a requirement of a mandatory service (with a caveat that those who are neglecting this honorable duty would not be received at court, etc.) and in 1785 Catherine II expanded this law by defining the individual (freedom from torture and bodily punishment, right to be judged only by the peers, unlimited right of ownership including serfs and commercial property, freedom from a personal taxation) and class (right to create the Noble Assemblies with the elective representatives which could have their own financial institutions and a right to send their proposals to the emperor) rights. But it took the decades for these laws to produce the "fruits" in the terms of splitting the nobility into serving and estate categories and changing social composition of the Guards (by the late XVIII nobility did not serve in the ranks and the Guards became just the ordinary ...er... "guards"). Keeping in mind that all relevant credit institutions of OTL (Noble Land Bank, Peasant Land Bank, etc.) had been an issue of a remote future, government simply did not have means to compensate nobility for the losses.
(d) General recognition of the need in reform simply was not there. When Catherine II tested this idea during the work of her Constitutional Assembly it was found that not only nobility but the merchants as well are against this idea. Actually, the merchants were asking for giving them a right to have serfs because they considered serfs much more reliable and trustworthy than the hired labor. Also, with the true industrial revolution (as in the "age of the steam") being a matter of the future, disadvantages of the serfdom in manufacturing were not quite obvious and economic factor was not there.
To make the long story short, Peter III would be assassinated if he tried to push this through. Even if he survived, the resulting mess would be terrible just due to the absent supporting framework. But if all these problems could be resolved by a click of the fingers, then by the early XIX Russia may become one of the most advanced states in Europe (its metallurgy was already quite developed).