As others have already noted, the question has both regulatory and technical aspects. This answer considers the technical aspects primarily, but includes some regulatory background information. Because regulations change and vary by locale, any future readers of this answer should look for the most current local regulatory information rather than relying solely on information here.
So with that said, let's look at the heart of the question:
My question is, can every amount of energy be fed into the grid for a remuneration according to the Feed-in-Tariff or should the electricity be first accumulated (using an energy storage system) to, lets say a kWh, or is any quantity possible to be fed back?
There are a couple of ways to interpret this, so to give a complete answer, I'll rephrase individual aspects of the question and answer each one separately.
Can every amount of energy be fed into the grid?
The answer to this is generally "no" from both a regulatory and technical viewpoint.
From the regulatory aspect, many Feed-In Tariff (FIT) schemes impose a cap on the size of a photovoltaic (PV) system that is eligible. For instance, the Los Angeles Department of Power & Water has a commercial PV size range of 30 kW to 3 MW for their current FIT
From a technical aspect, distribution systems, which is generally the term used to describe the part of the electric grid from the substation to individual homes or businesses, have physical limits as to the current they can carry. A typical distribution transformer, like the one that feeds my house, also has an associated fuse and the fuse represents a hard limit on power. The one on "my" transformer is rated 10A at 14.4kV, which is the distribution voltage in this area.
Should the electric energy be stored in integral kWh amounts?
Batteries are a very useful adjunct to PV systems. Obviously, PV systems only generate during the day when the sun is shining, so having a way to store some of that energy for later use is extremely useful to be able to continue to use energy when the sun is not shining. However, from a regulatory viewpoint, I don't know of any currently available FIT that requires the use of a storage systems. I think what might actually be meant by this question is the next interpretation.
What is the smallest increment that can be measured by a net meter?
The use of a net meter is often used in association with a FIT. In the old days, energy only went one way -- from a utility's generation plant toward the end users of that energy. Meters designed for that scenario measure kWh in one direction only. With a two-way flow of power in the scenario in which sometimes the energy goes from the grid into your house and sometimes energy goes to the grid from your own local generation, what is often used is a net meter. As suggested in the name it registers the net energy (supplied minus delivered) which can then be used to calculate the bill (or payment!) based on the current tariff, which might be a FIT. Meters for that purpose are generally very accurate -- a typical residential meter in North America is an ANSI standard class 0.2 meter which basically means that its measurement is within 0.2% of the true value. These meters also have a starting load requirement from the same standard which is 0.1A for the typical 200A circuit, which means that a current as low as 100mA (at 240V, that's 24W or 0.024kW) is enough to be measured accurately. For that reason, there are essentially no technical or regulatory limits on the smallest amount of energy that can be fed back into the grid.
I hope that that thoroughly answers your questions. If not, feel free to leave a comment and I'll try to address any aspects not yet covered.