A debt management, is a process where you come to an agreement with creditors to repay your debts. This is a non binding agreement to which the lenders don't have to accept your offer of repayment, nor are they legally obliged to agree or stick to the agreement. If the lenders don't like to offer of repayment, then they still have the option of taking you to court, issuing a CCJ etc.
An IVA, you need to qualify for however, you need a minimum debt of £15k. Lenders will always say to "avoid this" as it only lasts for 5 years, and what ever is still outstanding is written off. It's the last line before bankruptcy.
With regards to debt management, this will affect your credit file, potentially defaults may be registered against you by your lenders, some may update the file with "debt management", this will impact your ability to obtain credit, potentially affect any finacial associations you have, lower your credit score, increase rates for credit you may apply for in the future, as everything is on a "rate for risk", you would therefore be classed as a higher risk.
I'm a little confused by the calculations though. £10k at £200 pcm, would only repay £9,600. However, if there is a 16% managment fee, then you are only pay £168 pcm, mean in 4 years you will only have paid back £8,064. The managment fee is the monthly charge that the company you are with will take. Payment for it's services. I would question the figures as I smell a rat somewhere, it will take you a lot longer to clear the balances.
Lenders are under no legal obligation to freeze interest or charges, so in theory it will take longer than 4 years to clear the balances you owe.
In answer to your question regarding getting a mortgage, that to be fair is unanswerable. The current market, adverse lenders have pulled out, or limited the amount they will. It will all depend on the market at that time, if it's improved, what you credit status is, and, more importantly, if you have any CCJ registered against you.
Ensure you take independant advice first. Adverse credit, the current industry, it's all a mine field.