Is it true that power transformer has maximum efficiency at full load? In other words, is that possible practically?
All transformers are going to put out at least somewhat less power than is put in. In other words, there is no such thing as a perfect 100% efficient transformer (In real practical applications. Games can be played in a lab with superconducting materials and air cores to get close to 100% efficiency, but at best that's just for the transformer itself without system level considerations like how the power goes in and what happens to it after it comes out). Furthermore, in real transformers efficiency is traded off versus ultimate cost. It might be possible to make a particular transformer more effecient, but that would also cost more, possibly make it heavier, bigger, etc, so the manufacturer picked a tradeoff that they felt was best for the target market.
There will be some maximum efficiency for any model of transformer at various operating points, including at full load.
Or, if you're asking whether maximum efficiency occurs at full load, then probably not. The size of the core is one of the major cost factors of a transformer. Manufacturers aren't going to make it any bigger than necessary to meet the specs. The more power a transformer has to handle, all else kept constant, the bigger the core needs to be. Put another way, for any size transformer there will be a power level at which the core no longer acts "nicely" to allow for efficient operation. This doesn't happen abruptly at one point. Therefore at maximum power the not-nice effects are probably already starting at least a little bit. So to answer your question (if this is really what you asked), no, the maximum efficiency of most transformers is probably not at their maximum power level.
Of course the best way to determine this for any given transformer is to look at its datasheet.
The losses in a transformer comprise of fixed and variable. Fixed are not dependent on the load and are a function of the design( as Mr olin's note above-- design is also a compromise between cost and efficiency). Variable losses depend on the loading. Thus when seen per unit of load( efficiency), fixed losses will keep decreasing with increase in load while variable will increase, mostly in a non linear manner. Thus at some point of load the total losses will start increasing and that point is max efficiency point. This may not be max power point as max power point indicates the capacity of machine and not its efficiency