What made me confused is, the pKa is indicative of concentration of disscoiated relative ti undisscociated species. So when DMF has pKa of -0.3 it means it dissociates giving rise protons and conjugate (DMF without H+). However as you mentioned the pH of 0.5 M solution of DMF is 6.7. could you clarify more to abolish my misunderstanding.
Surely what could be happening is that below pH = -0.30 the carbonyl group of DMF is protonated by hyperacidic media and thus this solvent is acting as a cationic acid. After pH = -0.30 this proton is released and it therefore, along pH values from 0.0 to 14.0 at 298.2 K DMF is normaly acting in neutral way.
Similar to in aqueous solvents, the most basic (least acidic) group will be protonated by HCl, provided the reaction is downhill.
HCl is a difficult acid to give you an answer for because the acidity of HCl in DMF will depend on the amount of water present.
Lets take triflic acid instead, which is a very strong acid and will be able to protonate both DMF and Aniline;
The pKa of protonated DMF in DMF is, by definition, 0, similar to the pKa of H3O+ in H2O being 0. This is how pKa scales are usually referenced, with the pKa scale being defined by the free energy change of the following reaction in DMF;
2 DMF -> [DMF-H]+ + [DMF]-
This reaction is much less favorable than the equivalent reaction for water which brackets the pKa scale to 14;
2 H2O -> [H3O]+ + [OH]- (Keq = 10^-14).
This is generally why nonaqueous solvents have such larger pKa scales. In DMF the pKa scale is >20, from what I recall.
Going back to your question, the protonation of a mixture containing excess aniline and DMF relative to HOTf will only protonate the aniline after equilibrium has been acheived. This is because the pKa of aniline is ~ 2-3 in DMF, whereas the pKa of protonated DMF is 0. Even if DMF is initially protonated, the reaction
If pKa is negative it means the acid form of the conjugated pair (HDMF+, protonation at the nitrogen) is a strong acid, i.e. it does not exist in water. You woulds need to go to negative pH values [H+] larger than 1M to protonate DMF. In other words, the conjugated base, DMF, has a non-basic character in water.