What is the resolution down to which the annual inflation value can be controlled? Judging by previous posts in the site, the inflation target is set annually to 2% by the Federal Reserve. Regardless of the reasons behind this choice, I am curious to understand how precisely can the Federal Reserve aim for a value (maybe understanding the means they use to control it will be enlightening for that purpose). Could it be set, for the sake of the example, to 1.9% instead? Or to 1.95%?
What is the resolution down to which the annual inflation value can be controlled?

They can target arbitrary number. For example, they can target $1.9999\%$ or $3.1415\%$.

Could it be set, for the sake of the example, to 1.9% instead? Or to 1.95%?

Yes, it could. However, the target inflation rate is more or less aspirational and it is the value Fed aims to hit on average over the business cycle rather than maintain it at all times (in fact the target is not just $2\%$ but $2\%$ over the long run (see official Fed explanation here). Fed has dual mandate of keeping price stability and full employment. Following both of these objectives requires that inflation is sometimes above $2\%$ and sometimes below. In fact recently Fed chairman announced that in the near term they want to target inflation moderately above $2\%$.
In addition, note that Fed is not expected to hit its target with surgical precision. Consequently, there is not much point in setting it to $1.95\%$. For example, if Fed would keep the $2\%$ but inflation over long-run would happen to average at $1.95\%$ they would likely consider it a success since it is close enough to their target. Even though Fed can control inflation, price level (change in which gives you inflation) depends also on random macroeconomic perturbances/shocks. Consequently, most economists would not consider it a failure if average inflation deviates from its long run target by just $0.5\%$.
Regarding the means Fed has to control inflation there are several ones. Following, Blanchard et al. Macroeconomics central banks can control inflation via:

It can do it via changes in the interest rates (this is one of the most common ways).
Direct changes to the money supply.
Changes to the reserve requirement (currently abolished in the US).

An important caveat is that Fed is also institutionally constrained in the use of the above. For example, helicopter money is one way how central bank could expand money supply from economic perspective, but it might not be legal in the US (it is highly questionable). Fed can still affect money supply in other ways such as open market operations but these constraints mean that sometimes Fed cannot go as far as it would want with expansion of money supply.
Some other instruments are constrained by economic reality. For example, Fed cannot set interest rates too low as there is effective lower bound on how low the Fed funds rate can go. Typically models show it is at zero interest rate (although practically it is possible to go bit below) because cash has implicit $0\%$ interest rate and thus if Fed would set its rate significantly below zero (which would make commercial banks to go below zero as well) people would just refuse to keep their money in their banks and just keep cash (the interest rate can go bit negative as there are storage costs for keeping large sums of cash at home).
However, going over every minutiae detail of how Fed is constrained by law or economics would be beyond the scope of SE answer, but you should keep in mind that there are asterisks to the above.