Is the haloform reaction possible with fluorine and pseudohalogens also?
TL;Dr: Highly unlikely to be made using the general haloform reaction.
Long answer:
The mechanism of haloform reaction involves hypohalite ions resulting from the reaction between the base and the halogen.
$$\ce{X2 + NaOH -&gt; X- + XO- + H2O}$$
If we use fluorine as halogen, the resulting reaction will produce hypofluorite ion but this ion is extremely unstable and as such fluoroform can't be made using this reaction.  Trifluouromethane is known and used industrially in the manufacture of polytetrafluoroethylene (&quot;Teflon&quot;), but it is commonly made by anion exchange with another haloform, typically chloroform plus $\ce{HF}$.

For many years, chemists have been unable to isolate cyanoform as a neat, free acid. However, in September 2015, it was successfully isolated by a team of scientists at Ludwig Maximilian University of Munich. It is stable at temperatures below – 40 °C. So, it requires drastic conditions to synthesize cyanoform and is only stable at low temperatures. So, it is highly unlikely to be made at ambient conditions using laboratory grade reagents.

Nitroform has been made in the laboratory by the hydrolysis of tetranitromethane under mild basic conditions. But can it be made using general haloform reaction? Yes, it can technically be made but there are face several problems. Let's start with the starting reaction i.e. reaction between base and nitrogen dioxide which produces nitrite and nitrate ions:
$$\ce{2OH- + 2NO2 -&gt; NO2- + NO3- + H2O (+other nitrogen oxides)}$$

The nitrite that forms is not that great reactive oxidizer.
There might be an undesirable side reaction which is kind of a Meyer reaction to form undesirable nitrolic acid/psudonitrol which in basic conditions gives blood red/blue colored solution.
The reaction involves huge amount of nitrogen oxides in general which is not very economical to deal with.
Multiple SN1 reactions occurs that generates a lot of isomers and other nitro compounds of compounds along with a whole lot of nitrite esters.
Steric hindrance might play a role and the reaction would not proceed properly.
The nitroformate ion ($\ce{C(NO2)3^-}$) might ionize to form different ions: $\ce{CH(NO2)2^-}$, $\ce{CH2NO2^-}$.
Nitroform is itself a strong oxidizer.

There are discussions in forums regarding trinitromethane synthesis using general haloform reaction but this ended up being fruitless. It even discussed using copper salts as catalyst and even employed haloform itself to react with $\ce{Ag/NaNO2}$ in DMF/ether but these syntheses posed so much problems and the yield was generally very, very poor.