Burden of debt; Internal or external financing? Q1) How does the burden of an external public debt differ from that of an internal public debt?
Q2) Are there sny conditions under which neither external  nor internal debt is a burden to a nation?
Q1 : If you define external debt as "forex debt" context. 
If the debt repayment amount for every period are greater than a country import/export amount, then it will influence the exchange rate.  Subsequently affect goods price. 

For internal debt (e.g. money borrow within the country, using various financial tools or creative derivative ). 
On positive side, if the debt spending bring in long term production or/and cost saving benefit, it will be reduce the debt burden, increase income. As it suppose to get the debt payoff from the positive benefit. 

On negative side, internal debt can be wasted, or lead to speculative activities. In such case, the problem can be many folds, depends on the magnitude of of the debt. For "smaller scale", creditor or so call "investor" lost their money. E.g. Enron, Worldcomm scandal.
For the worst snowball case, the effect is much dire and difficult to assess. E.g. the worst private sector debt, you can check out example of subprime mortgage crisis. For country level, you can check out the Greek government-debt crisis.   

Q2 : Under perfect world production context (no production of unwanted goods, goods/finance speculation/corruption), as long as the production income are more than the debt, there will be no ill effect from borrowing.  

Note : In each economic question, context is always required, no matter how you apply famous/infamous economist that apply math formula. Because human society keep adapting and exploiting the system.