However to enable/guide you in how you might go about screening for self primer interactions, i.e. F:F and R;R, whether hair pin loops or linear duplex annealing I would and do access the following sites:
For F;R that is heterodimer formation leading potentially to primer dimers, the above Oligo calculator makes no provision. I therefore use the following excellent tool by IDT:
2. https://www.idtdna.com/calc/analyser
The latter predicts actual stability of putative structures based on Gibbs free energy (Delta G): In essence, if a structure is predicted to have a Delta G < -10kCal/mol that means in real time it might exist in a steady state form and thus pose a real problem in terms of primer dimer formation
Structures with Delta G > -10kCal/mol are not likely to exist in any real sense and are thus more theoretical then real for the duration of the reaction and thus do not culminate in any substantial primer dimers (that is that could form but then just as quickly fall apart)
In terms of primer design by simply avoiding runs of 3 or more G/C residues at the ends of primers or areas within primers that have more than 3 G/C residues you will probably avoid predicted steady state primer dimers (as defined by their delta g value in Kcal/mol)
Similalrly, if you have G and C residues that are predicted to hybridise but they are interspersed with bases that are not complimentary, once again such structures are more theoretical than real and pose no tangible risk in an actual PCR reaction
Finally, when it comes to contiguous runs of A and T residues simply ignore
Find attached a doc that will help you with these and other issues
I should add that primer 3 does look for F;F; R:R and F;R self and heterodimers when it designs primers but none the less I tend to confirm using the above