1. Identify where hydrogen bonding is important

Hydrogen bonding can affect:

• intermolecular association,
• solvation in water,
• structural arrangement of molecules,
• stability of conjugate bases or molecular aggregates.

We evaluate each option independently.

2. Option A: ice floats in water

In ice, water molecules form an open three-dimensional hydrogen-bonded network. This makes ice less dense than liquid water.

Since density of ice is lower than density of water, ice floats.

So, A is correct.

3. Option B: higher Lewis basicity of primary amines than tertiary amines in aqueous solutions

In aqueous solution, basicity is not decided only by the $+I$ effect of alkyl groups; it also depends strongly on solvation of the protonated amine by water.

Primary amines form conjugate acids such as $RNH_3^+$, which are better solvated through hydrogen bonding with water than tertiary ammonium ions such as $R_3NH^+$.

Tertiary amines suffer from steric hindrance, so hydrogen bonding/solvation by water is less effective. Hence, in aqueous solution, primary amines can be more basic than tertiary amines.

Therefore, hydrogen bonding plays a central role here.

So, B is correct.

4. Option C: formic acid is more acidic than acetic acid

We compare:

• formic acid: $HCOOH$
• acetic acid: $CH_3COOH$

The methyl group in acetic acid shows a $+I$ effect, which destabilizes the acetate ion relative to formate ion, making acetic acid weaker than formic acid.

Also, in aqueous medium, the conjugate base $HCOO^-$ is better hydrated via hydrogen bonding than $CH_3COO^-$ because the methyl group reduces effective hydration somewhat.

Thus hydrogen bonding/solvation contributes to the greater acidity of formic acid.

So, C is correct.

5. Option D: dimerisation of acetic acid in benzene

In nonpolar solvents such as benzene, acetic acid molecules associate to form cyclic dimers through intermolecular hydrogen bonding:

$2\,CH_3COOH \rightleftharpoons (CH_3COOH)_2$

This dimerisation is a classic consequence of hydrogen bonding.

So, D is correct.

6. Final selection

All four phenomena involve hydrogen bonding significantly.

Hence the correct options are:

$\boxed{A,\ B,\ C,\ D}$

7. Comparison with stored correct answer

Stored correct answer: $A, B, C, D$

My derived answer matches the stored correct answer.