Yes you can lend part of this money to your SMSF so that the SMSF can buy an investment property or other investments such as shares. However, the loan to your SMSF must be at commercial rates, at arms length and be of limited recourse in nature.
As the loan to your SMSF would be of limited recourse nature it may require you to charge a premium above the full recourse rate that you are paying on your mortgage outside of the SMSF. It is best for you to look at similar prevailing interest rates charges by major banks to SMSFs and use these rates as a benchmark for what rate you charge your SMSF - this way you can show you are using commercial rates.
The limited recourse nature of the loan is unlikely to attract a lower rate than your home loan, so charging less than you are paying is unlikely to be acceptable to the ATO. The ATO may also be concerned that you are attempting to circumvent the contribution limits and are putting excess amounts into your super fund. If you set up these arrangements incorrectly there may be serious tax implications for both yourself and your SMSF.
In essence, your SMSF can claim a tax deduction against the interest it pays you for the loan and you would make a profit (gain) from the interest you collect from your SMSF minus the interest you pay your bank for your mortgage. So your SMSF would get a tax deduction at the tax rate of 15% but you would pay tax at your marginal tax rate (usually higher than 15% unless you earn very little income).
So for your Q2. If so, can I deduct the interest paid by SMSF to me, and deduct under my name, as I would when I buy an investment property outside SMSF? No your SMSF (being a separate entity) would deduct this interest paid by the SMSF not you, you would actually include it as income under your tax return.