Is it possible to load Windows 10 Home onto a computer with Windows 7 Pro without losing acces to the installed programs?
No.; it isn't possible.
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Windows 10 supported upgrade paths:
✔ = Full upgrade is supported including personal data, settings, and applications.
D = Edition downgrade; personal data is maintained, applications and settings are removed.
https://docs.microsoft.com/en-us/windows/deployment/upgrade/windows-10-upgrade-paths
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| Windows 10 Home | Windows 10 Pro | Windows 10 Pro Education | Windows 10 Education | Windows 10 Enterprise | Windows 10 Mobile | Windows 10 Mobile Enterprise | ||
|---|---|---|---|---|---|---|---|---|
| Windows 7 | ||||||||
| Starter | ✔ | ✔ | ✔ | ✔ | ||||
| Home Basic | ✔ | ✔ | ✔ | ✔ | ||||
| Home Premium | ✔ | ✔ | ✔ | ✔ | ||||
| Professional | D | ✔ | ✔ | ✔ | ✔ | |||
| Ultimate | D | ✔ | ✔ | ✔ | ✔ | |||
| Enterprise | ✔ | ✔ |