I believe that you may have done the calculation incorrectly, but I am not completely sure that I understand your questions. First, the Target Hazard Quotient is typically defined as a goal or decision criterion, and is often set to 1 (as a matter of policy, or the goals of the risk manager). The calculated HQ is compared to the THQ to determine whether or not the potential for noncancer effects warrants action and/or further analysis (e.g., above the THQ = bad). If the EDI is greater than the RfD, that means that the applied dose is above the reference dose, so the HQ should be greater than 1 (and, therefore, greater than the THQ). It could be that you flipped numerator and denominator and, if you did, you would be far from the first person to do that.

With regard to your second question, cancer risk is typically expressed as a probability (e.g., 1 in 100,000 excess risk of cancer) although one can certainly perform the calculation as an HQ (you could argue with risk assessors about that for a long time). That said, a cancer risk of 1 in a 100 should result in a very high HQ if you are using a target cancer risk of, say, 10^-6 since there is a three order of magnitude difference. This may be the same issue, namely, that you have inadvertently flipped numerator and denominator.

I would set up your equations with just the units and walk through it. That may reveal where the issue is with your calculation. Hope this was helpful.

Conventionally, the term "target hazard quotient" is used to define the hazard quotient that is deemed to be acceptable, i.e., for the calculation of a screening level, a remedial concentration, or a threshold of acceptable hazard in a forward risk assessment.  Therefore, the "target HQ" stays the same, irrespective of the estimated chemical-specific HQ that you derived on the basis of your estimated daily intake (EDI).  If the estimated daily intake from a predicted exposure (EDI) exceeds the RfD, then the estimated chemical-specific hazard quotient for that exposure does indeed exceed 1 (unity).  If the target hazard quotient was established as some value less than one (e.g., to calculate a screening level, or to account for multiple chemicals with the same target organ or mode of action), then the estimated chemical-specific HQ will exceed the target HQ.  

With respect to your second question, I think it is important to remember that the calculation of non-cancer hazard and cancer risk are independent functions; cancer effects and non-cancer effects are evaluated (for the time being, at least) as separate endpoints. The relative toxicity of the separate endpoints can vary by orders of magnitude; this difference may therefore be reflected in the respective chemical-specific hazard quotient and chemical-specific excess lifetime cancer risk.  Although I am not familiar with the particulars of your exposure assessment, or of the toxicity factors you used, this type of result your reported for nickel is somewhat surprising.  You may want to check and see whether you are comparing a estimated chemical-specific HQ based on the oral route of exposure (ingestion) with a chemical-specific estimated ELCR for the respiratory route of exposure (inhalation).  To the best of my knowledge, in most of the world, nickel is only considered to be carcinogenic via the inhalation route of exposure. 

Please check I use this data:

I provide you the exact data which I used in my calculation. Please tell me at which point I am wrong. I shall be highly obliged to you.

 I used these values in these following equations:

EDI=(Mc ×IR)/Bw

THQ=(Mc × IR ×10^-3 ×EF × ED)/(RfD×BW×ATn)

Where, EDI= estimated daily intake

THQ is for non-carcinogenic risk

MC is the metal concentration in fish (Ni) = 7.91(mg/kg.dry weight)

IR is the fish ingestion rate (g/day). An average Indian adult consumes fish approximately 19.5 g/day (Speedy, 2003; Little et al., 2002) and this consumption rate was used in our health-risk assessment.

EF is the exposure frequency (days/year) (5 days week-1 or 240 days/year)

ED is the exposure duration over lifetime (30 years) USEPA (1989) assumptions.

RfD is the reference dose of Ni =2.0×10^-2 (mg/kg/day) (USEPA, 2012)

BW is an average body weight of Indian male is 57 kg and that of female is 50 kg (Shukla et al., 2002)

ATn is the averaging time for non-carcinogens (365 days/year × 30 years = 10950 days) (USEPA, 2011)

For TR

TR=(Mc × IR ×10^-3 ×CPSo × EF × ED)/(BW × ATc)

Where ATc is the averaging time for carcinogens (365days/year × 67 = 24455 days), since the average life expectancy for males is 65 years (approx.) and for females is 68 years (approx.) in India, therefore an average of two has taken.